Structural complexity metrics for UML class diagrams

In order to evaluate the structural complexity of class diagrams systematically and deeply, a new guiding framework of structural complexity is presented. An index system of structural complexity for class diagrams is given. This article discusses the formal description of class diagrams, and presents the method of formally structural complexity metrics for class diagrams from associations, dependencies, aggregations, generalizations and so on. An applicable example proves the feasibility of the presented method.

Block-based test data adequacy measurement criteria and test complexity metrics

On the basis of software testing tools we developed for programming languages, we firstly present a new control flowgraph model based on block. In view of the notion of block, we extend the traditional program\|based software test data adequacy measurement criteria, and empirically analyze the subsume relation between these measurement criteria. Then, we define four test complexity metrics based on block. They are J\|complexity 0; J\|complexity 1; J\|complexity \{1+\}; J\|complexity 2. Finally, we show the Kiviat diagram that makes software quality visible.

Research of Software Complexity Metrics with Security Indicator

Software protection technology has been universally emphasized, with the development of reverse engineering and static analysis techniques. So, it is important to research how to quantitatively evaluate the security of the protected software. However, there are some researchers evaluating the security of the proposed protect techniques directly by the traditional complexity metrics, which is not suffident. In order to better reflect security from software complexity, a multi-factor complexity metric based on control flow graph （CFG） is proposed, and the corresponding calculating procedures are presented in detail. Moreover, complexity density models are constructed to indicate the strength of software resisting reverse engineering and code analysis. Instance analysis shows that the proposed method is simple and practical, and can more objectively reflect software security from the perspective of the complexity.

A Hybrid Set of Complexity Metrics for Large-Scale Object-Oriented Software Systems

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.

Study of Complex TOUGMA’s Metric

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.

Orbits of Material Bodies in Complex TOUGMA’s Metric

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.

B-Implicit Contractive Conditions and Unique（Common） Fixed Points on Complex Valued Metric Spaces

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.

Points of Coincidence and Common Fixed Points for Ⅱ-Expansive Mappings on Complex Valued Metric Spaces

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.

Einstein Energy-Momentum Complex for a Phantom Black Hole Metric

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.

ON DOUBLY WARPED PRODUCT OF COMPLEX FINSLER MANIFOLDS

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.

Locally Conformal Pseudo-Kahler Finsler Manifolds

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.

A New Method for Measurement and Reduction of Software Complexity

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.

Khler Finsler Metrics Are Actually Strongly Khler

In this paper, the Kahler conditions of the Chern-Finsler connection in complex Finsler geometry are studied, and it is proved that Kahler Finsler metrics are actually strongly Kahler.

On U(n)-invariant strongly convex complex Finsler metrics

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).

On Unitary Invariant Weakly Complex Berwald Metrics with Vanishing Holomorphic Curvature and Closed Geodesics

In this paper, the authors construct a class of unitary invariant strongly pseudoconvex complex Finsler metrics which are of the form F =√[ rf(s- t)[, where r = ||v||~ 2, s =| z,v |~2/r, t =|| z||~ 2, f(w) is a real-valued smooth positive function of w ∈ R,and z is in a unitary invariant domain M C^n. Complex Finsler metrics of this form are unitary invariant. We prove that F is a class of weakly complex Berwald metrics whose holomorphic curvature and Ricci scalar curvature vanish identically and are independent of the choice of the function f. Under initial value conditions on f and its derivative f, we prove that all the real geodesics of F =√[rf(s- t)] on every Euclidean sphere S^(2n-1) M are great circles.

Strongly convex weakly complex Berwald metrics and real Landsberg metrics

Under the assumption that' is a strongly convex weakly Khler Finsler metric on a complex manifold M, we prove that F is a weakly complex Berwald metric if and only if F is a real Landsberg metric.This result together with Zhong(2011) implies that among the strongly convex weakly Kahler Finsler metrics there does not exist unicorn metric in the sense of Bao(2007). We also give an explicit example of strongly convex Kahler Finsler metric which is simultaneously a complex Berwald metric, a complex Landsberg metric,a real Berwald metric, and a real Landsberg metric.

Laplacian on Complex Finsler Manifolds

In this paper, the Laplacian on the holomorphic tangent bundle T 1,0 M of a complex manifold M endowed with a strongly pseudoconvex complex Finsler metric is defined and its explicit expression is obtained by using the Chern Finsler connection associated with (M, F ). Utilizing the initiated "Bochner technique", a vanishing theorem for vector fields on the holomorphic tangent bundle T 1,0 M is obtained.

A New Peer-to-Peer Topology for Video Streaming Based on Complex Network Theory

A new wave of networks labeled Peer-to-Peer(P2P) networks attracts more researchers and rapidly becomes one of the most popular applications.In order to matching P2 P logical overlay network with physical topology,the position-based topology has been proposed.The proposed topology not only focuses on non-functional characteristics such as scalability,reliability,fault-tolerance,selforganization,decentralization and fairness,but also functional characteristics are addressed as well.The experimental results show that the hybrid complex topology achieves better characteristics than other complex networks' models like small-world and scale-free models;since most of the real-life networks are both scale-free and small-world networks,it may perform well in mimicking the reality.Meanwhile,it reveals that the authors improve average distance,diameter and clustering coefficient versus Chord and CAN topologies.Finally,the authors show that the proposed topology is the most robust model,against failures and attacks for nodes and edges,versus small-world and scale-free networks.