Large-scale object-oriented(OO) software systems have recently been found to share global network characteristics such as small world and scale free,which go beyond the scope of traditional software measurement and ...Large-scale object-oriented(OO) software systems have recently been found to share global network characteristics such as small world and scale free,which go beyond the scope of traditional software measurement and assessment methodologies.To measure the complexity at various levels of granularity,namely graph,class(and object) and source code,we propose a hierarchical set of metrics in terms of coupling and cohesion-the most important characteristics of software,and analyze a sample of 12 open-source OO software systems to empirically validate the set.Experimental results of the correlations between cross-level metrics indicate that the graph measures of our set complement traditional software metrics well from the viewpoint of network thinking,and provide more effective information about fault-prone classes in practice.展开更多
General relativity of Einstein’s theory and Quantum physics theory are excellent pillars that explain much modern physics. Understanding the relation between these theories is still a theoretical physics central open...General relativity of Einstein’s theory and Quantum physics theory are excellent pillars that explain much modern physics. Understanding the relation between these theories is still a theoretical physics central open question. Over last several decades, works in this direction have led to new physical ideas and mathematical tools broad range. In recent years TOUGMA’s equation is established and solved, one of its solutions such as a real solution is studied in our last article. In this paper, complex TOUGMA’s metric is studied, particularly the physics concepts that this metric implies such as light geodesic and metric’s impacts at r = 0. The first time, we studied the fact of r = 0 and its limits, secondly, we consider a zero length light geodesic is a geodesic and ended by studying it mathematically. These underlying principles study, those various phenomena in universe are interconnected logic leading to develop new technologies for example: news engines, telecommunication networks. This study’s applications are exceptionally wide such as Astrophysics, cosmology, Quantum gravity, Quantum Mechanics, Multiverse. Mostly this study lets us to know the quantum relativity universe behaviors.展开更多
Einstein’s General relativity theory and Quantum physics are the main pillars for explaining most modern physics. Obtaining these theories relation between them remains a theoretical physics main question. In the las...Einstein’s General relativity theory and Quantum physics are the main pillars for explaining most modern physics. Obtaining these theories relation between them remains a theoretical physics main question. In the last most decades, works are leading to new physical ideas and mathematical tools broad range. In recent years TOUGMA’s equation is established and solved, and one of these solutions, mostly a real solution is studied in our last article. In this work, complex TOUGMA’s metric is studied, such as the physics concepts implied by this metric, mainly material bodies geodesics orbits. We studied the fact material bodies’ orbits and their limits. This study of the underlying principles and various phenomena in universe are interconnected logic leading to new technologies development such as news engines and telecommunication networks. The applications of this study are exceptionally wide such as Astrophysics, cosmology, Quantum gravity, Quantum Mechanics and Multiverse. Mostly this study allows us to know the behaviors of matter in the quantum relativity universe. Universe.展开更多
A class B of complex functions is introduced and several existence theorems of unique(common) fixed points for mappings satisfying a B-implicit contraction are presented.Moreover, the existence results of common fixed...A class B of complex functions is introduced and several existence theorems of unique(common) fixed points for mappings satisfying a B-implicit contraction are presented.Moreover, the existence results of common fixed points for two mappings on a nonempty set with two complex valued metrics are provided. Our outcomes generalize and improve some known results, especially, for instance, Banach contraction principle, Chatterjea-type fixed point theorem and the corresponding fixed point theorems.展开更多
Abstract. We use the two mappings satisfying II-expansive conditions on complex valued metric spaces to construct the convergent sequences and prove that the unique limit of the sequences is the point of coincidence o...Abstract. We use the two mappings satisfying II-expansive conditions on complex valued metric spaces to construct the convergent sequences and prove that the unique limit of the sequences is the point of coincidence or common fixed point of the two mappings. Also, we discuss the uniqueness of points of coincidence or common fixed points and give the existence theorems of unique fixed points. The obtained results generalize and improve the corresponding conclusions in references.展开更多
We calculate the energy distribution associated with a static spherically symmetric non-singular phantom black hole metric in Einstein's prescription in general relativity. As required for the Einstein energy-momentu...We calculate the energy distribution associated with a static spherically symmetric non-singular phantom black hole metric in Einstein's prescription in general relativity. As required for the Einstein energy-momentum complex, we perform the calculations in quasi-Cartesian coordinates. We also calculate the momentum components and obtain a zero value, as expected from the geometry of the metric.展开更多
Let (M1, F1) and (M2, F2) be two strongly pseudoconvex complex Finsler man- ifolds. The doubly wraped product complex Finsler manifold (f2 M1 x h M2, F) of (M1, F1) and (M2, F2) is the product manifold M1 x ...Let (M1, F1) and (M2, F2) be two strongly pseudoconvex complex Finsler man- ifolds. The doubly wraped product complex Finsler manifold (f2 M1 x h M2, F) of (M1, F1) and (M2, F2) is the product manifold M1 x M2 endowed with the warped product complex 2 2 Finsler metric F2 = f2F1 + fl F2, where fl and f2 are positive smooth functions on M1 and M2, respectively. In this paper, the most often used complex Finsler connections, holomorphic curvature, Ricci scalar curvature, and real geodesics of the DWP-complex Finsler manifold are derived in terms of the corresponding objects of its components. Necessary and sufficient conditions for the DWP-complex Finsler manifold to be K/ihler Finsler (resp., weakly K/ihler Finsler, complex Berwald, weakly complex Berwald, complex Landsberg) manifold are ob- tained, respectively. It is proved that if (M1, F1) and (M2,F2) are projectively flat, then the DWP-complex Finsler manifold is projectively flat if and only if fl and f2 are positive constants.展开更多
In this paper,we give a necessary and sucient condition for a strongly pseudoconvex complex Finsler metric to be locally conformal pseudo-Kahler Finsler.As an application,we nd any complete strongly convex and local...In this paper,we give a necessary and sucient condition for a strongly pseudoconvex complex Finsler metric to be locally conformal pseudo-Kahler Finsler.As an application,we nd any complete strongly convex and locally conformal pseudo-Kahler Finsler manifold,which is simply connected or whose fundamental group contains elements of nite order only,can be given a Kahler metric.展开更多
This paper develops an improved structural software complexity metrics named information flow complexity which is closely related to the reliability of software. Together with the three software complexity metrics, th...This paper develops an improved structural software complexity metrics named information flow complexity which is closely related to the reliability of software. Together with the three software complexity metrics, the total software complexity is measured and some rules to reduce the complexity are presented in the paper. To illustrate and explain the process of measurement and reduction of software complexity, several examples and experiments are given. It is proposed that software complexity metrics can be measured earlier in software development and can provide substantial information of software systems whose reliabil- ity can be modeled and used in the determination of initial parameter estimation.展开更多
In this paper,we obtain a necessary and sufficient condition for a U(n)-invariant complex Finsler metric F on domains in C^(n) to be strongly convex,which also makes it possible to investigate the relationship between...In this paper,we obtain a necessary and sufficient condition for a U(n)-invariant complex Finsler metric F on domains in C^(n) to be strongly convex,which also makes it possible to investigate the relationship between real and complex Finsler geometries via concrete and computable examples.We prove a rigid theorem which states that a U(n)-invariant strongly convex complex Finsler metric F is a real Berwald metric if and only if F comes from a U(n)-invariant Hermitian metric.We give a characterization of U(n)-invariant weakly complex Berwald metrics with vanishing holomorphic sectional curvature and obtain an explicit formula for holomorphic curvature of the U(n)-invariant strongly pseudoconvex complex Finsler metric.Finally,we prove that the real geodesics of some U(n)-invariant complex Finsler metric restricted on the unit sphere S^(2n-1)■C^(n) share a specific property as that of the complex Wrona metric on C^(n).展开更多
基金Supported by the National Grand Fundamental Research 973 Program of China under Grant No.2007CB310800the National Natural Science Foundation of China under Grant Nos.60873083 and 60803025+2 种基金the Research Fund for the Doctoral Program of Higher Education of China under Grant No.20090141120022the Natural Science Foundation of Hubei Province of China under Grant Nos.2008ABA379 and 2008CDB351the Fundamental Research Funds for the Central Universities of China under Grant No.6082005
文摘Large-scale object-oriented(OO) software systems have recently been found to share global network characteristics such as small world and scale free,which go beyond the scope of traditional software measurement and assessment methodologies.To measure the complexity at various levels of granularity,namely graph,class(and object) and source code,we propose a hierarchical set of metrics in terms of coupling and cohesion-the most important characteristics of software,and analyze a sample of 12 open-source OO software systems to empirically validate the set.Experimental results of the correlations between cross-level metrics indicate that the graph measures of our set complement traditional software metrics well from the viewpoint of network thinking,and provide more effective information about fault-prone classes in practice.
文摘General relativity of Einstein’s theory and Quantum physics theory are excellent pillars that explain much modern physics. Understanding the relation between these theories is still a theoretical physics central open question. Over last several decades, works in this direction have led to new physical ideas and mathematical tools broad range. In recent years TOUGMA’s equation is established and solved, one of its solutions such as a real solution is studied in our last article. In this paper, complex TOUGMA’s metric is studied, particularly the physics concepts that this metric implies such as light geodesic and metric’s impacts at r = 0. The first time, we studied the fact of r = 0 and its limits, secondly, we consider a zero length light geodesic is a geodesic and ended by studying it mathematically. These underlying principles study, those various phenomena in universe are interconnected logic leading to develop new technologies for example: news engines, telecommunication networks. This study’s applications are exceptionally wide such as Astrophysics, cosmology, Quantum gravity, Quantum Mechanics, Multiverse. Mostly this study lets us to know the quantum relativity universe behaviors.
文摘Einstein’s General relativity theory and Quantum physics are the main pillars for explaining most modern physics. Obtaining these theories relation between them remains a theoretical physics main question. In the last most decades, works are leading to new physical ideas and mathematical tools broad range. In recent years TOUGMA’s equation is established and solved, and one of these solutions, mostly a real solution is studied in our last article. In this work, complex TOUGMA’s metric is studied, such as the physics concepts implied by this metric, mainly material bodies geodesics orbits. We studied the fact material bodies’ orbits and their limits. This study of the underlying principles and various phenomena in universe are interconnected logic leading to new technologies development such as news engines and telecommunication networks. The applications of this study are exceptionally wide such as Astrophysics, cosmology, Quantum gravity, Quantum Mechanics and Multiverse. Mostly this study allows us to know the behaviors of matter in the quantum relativity universe. Universe.
文摘A class B of complex functions is introduced and several existence theorems of unique(common) fixed points for mappings satisfying a B-implicit contraction are presented.Moreover, the existence results of common fixed points for two mappings on a nonempty set with two complex valued metrics are provided. Our outcomes generalize and improve some known results, especially, for instance, Banach contraction principle, Chatterjea-type fixed point theorem and the corresponding fixed point theorems.
基金supported by the National Natural Science Foundation of China (No. 11361064)
文摘Abstract. We use the two mappings satisfying II-expansive conditions on complex valued metric spaces to construct the convergent sequences and prove that the unique limit of the sequences is the point of coincidence or common fixed point of the two mappings. Also, we discuss the uniqueness of points of coincidence or common fixed points and give the existence theorems of unique fixed points. The obtained results generalize and improve the corresponding conclusions in references.
文摘We calculate the energy distribution associated with a static spherically symmetric non-singular phantom black hole metric in Einstein's prescription in general relativity. As required for the Einstein energy-momentum complex, we perform the calculations in quasi-Cartesian coordinates. We also calculate the momentum components and obtain a zero value, as expected from the geometry of the metric.
基金supported by Program for New Century Excellent Talents in University(NCET-13-0510)National Natural Science Foundation of China(11271304,11571288,11461064)+1 种基金the Fujian Province Natural Science Funds for Distinguished Young Scholar(2013J06001)the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry
文摘Let (M1, F1) and (M2, F2) be two strongly pseudoconvex complex Finsler man- ifolds. The doubly wraped product complex Finsler manifold (f2 M1 x h M2, F) of (M1, F1) and (M2, F2) is the product manifold M1 x M2 endowed with the warped product complex 2 2 Finsler metric F2 = f2F1 + fl F2, where fl and f2 are positive smooth functions on M1 and M2, respectively. In this paper, the most often used complex Finsler connections, holomorphic curvature, Ricci scalar curvature, and real geodesics of the DWP-complex Finsler manifold are derived in terms of the corresponding objects of its components. Necessary and sufficient conditions for the DWP-complex Finsler manifold to be K/ihler Finsler (resp., weakly K/ihler Finsler, complex Berwald, weakly complex Berwald, complex Landsberg) manifold are ob- tained, respectively. It is proved that if (M1, F1) and (M2,F2) are projectively flat, then the DWP-complex Finsler manifold is projectively flat if and only if fl and f2 are positive constants.
基金Supported by the National Natural Science Foundation of China(Grant No.12001165)Postdoctoral Research Foundation of China(Grant No.2019M652513)Postdoctoral Research Foundation of Henan Province(Grant No.19030050).
文摘In this paper,we give a necessary and sucient condition for a strongly pseudoconvex complex Finsler metric to be locally conformal pseudo-Kahler Finsler.As an application,we nd any complete strongly convex and locally conformal pseudo-Kahler Finsler manifold,which is simply connected or whose fundamental group contains elements of nite order only,can be given a Kahler metric.
基金the National Natural Science Foundation of China (No. 60473033)
文摘This paper develops an improved structural software complexity metrics named information flow complexity which is closely related to the reliability of software. Together with the three software complexity metrics, the total software complexity is measured and some rules to reduce the complexity are presented in the paper. To illustrate and explain the process of measurement and reduction of software complexity, several examples and experiments are given. It is proposed that software complexity metrics can be measured earlier in software development and can provide substantial information of software systems whose reliabil- ity can be modeled and used in the determination of initial parameter estimation.
基金supported by National Natural Science Foundation of China(Grant No.11671330)the Nanhu Scholars Program for Young Scholars of Xinyang Normal Universitythe Scientific Research Fund Program for Young Scholars of Xinyang Normal University(Grant No.2017-QN-029)。
文摘In this paper,we obtain a necessary and sufficient condition for a U(n)-invariant complex Finsler metric F on domains in C^(n) to be strongly convex,which also makes it possible to investigate the relationship between real and complex Finsler geometries via concrete and computable examples.We prove a rigid theorem which states that a U(n)-invariant strongly convex complex Finsler metric F is a real Berwald metric if and only if F comes from a U(n)-invariant Hermitian metric.We give a characterization of U(n)-invariant weakly complex Berwald metrics with vanishing holomorphic sectional curvature and obtain an explicit formula for holomorphic curvature of the U(n)-invariant strongly pseudoconvex complex Finsler metric.Finally,we prove that the real geodesics of some U(n)-invariant complex Finsler metric restricted on the unit sphere S^(2n-1)■C^(n) share a specific property as that of the complex Wrona metric on C^(n).