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Research on Network Defense Graph Model in Network Security
Feng Qi,Haili Xu 보안공학연구지원센터 2016 International Journal of Security and Its Applicat Vol.10 No.11
Security analysis and attack-defense modeling are effective method to identify the vulnerabilities of information systems for proactive defense. The attack graph model reflects only attack actions and system state changes, without considering the perspective of the defenders. To assess the network information system and comprehensively show attack and defense strategies and theirs cost, a defense graph model is proposed. Compared with the attack graph, the model makes some improvements. Defense graph will be mapped to the attack and defense game model, in order to provide a basis for active defense policy decision. What’s more, a generation algorithm of defense graph is proposed. A representative example is provided to illustrate our models and generation algorithm.
COMPLETE MONOTONICITY OF A DIFFERENCE BETWEEN THE EXPONENTIAL AND TRIGAMMA FUNCTIONS
Feng Qi,Xiao-Jing Zhang 한국수학교육학회 2014 純粹 및 應用數學 Vol.21 No.2
In the paper, by directly verifying an inequality which gives a lowerbound for the first order modified Bessel function of the first kind, the authors supplya new proof for the complete monotonicity of a difference between the exponentialfunction e^(1/t) and the trigamma function ψ'(t) on (0, ∞).
Feng Qi,Qiu-Ming Luo,Bai-Ni Guo 한국수학교육학회 2004 純粹 및 應用數學 Vol.11 No.3
In this article, using the L'Hospital rule, mathematical induction, the trigonometric power formulae and integration by parts, some integral formulae for the improper integrals R1 0 [sin2m(��x)]=(x2n)dx and R1 0 [sin2m+1(��x)]=(x2n+1)dx are established, where m ¸ n are all positive integers and �� 6= 0.
Some properties of the Bernoulli numbers of the second kind and their generating function
Feng Qi,Jiao-Lian Zhao 대한수학회 2018 대한수학회보 Vol.55 No.6
In the paper, the authors find a common solution to three series of differential equations related to the generating function of the Bernoulli numbers of the second kind and present a recurrence relation, an explicit formula in terms of the Stirling numbers of the first kind, and a determinantal expression for the Bernoulli numbers of the second kind.
Four logarithmically completely monotonic functions involving gamma function
Feng Qi,Da-Wei Niu,Jian Cao,Shou-Xin Chen 대한수학회 2008 대한수학회지 Vol.45 No.2
In this paper, two classes of functions, involving a parameter and the classical Euler gamma function, and two functions, involving the classical Euler gamma function, are verified to be logarithmically completely monotonic in (-½, ∞) or (0, ∞); some inequalities involving the classical Euler gamma function are deduced and compared with those originating from certain problems of traffic flow, due to J. Wendel and A. Laforgia, and relating to the well known Stirling’s formula. In this paper, two classes of functions, involving a parameter and the classical Euler gamma function, and two functions, involving the classical Euler gamma function, are verified to be logarithmically completely monotonic in (-½, ∞) or (0, ∞); some inequalities involving the classical Euler gamma function are deduced and compared with those originating from certain problems of traffic flow, due to J. Wendel and A. Laforgia, and relating to the well known Stirling’s formula.
SOME LOGARITHMICALLY COMPLETELY MONOTONIC FUNCTIONS RELATED TO THE GAMMA FUNCTION
Feng Qi,Bai-Ni Guo 대한수학회 2010 대한수학회지 Vol.47 No.6
In this article, the logarithmically complete monotonicity of some functions such as [수식],[수식],[수식] and [수식]for α ∈ R on (−1,∞) or (0,∞) are obtained, some known results are recovered, extended and generalized. Moreover, some basic properties of the logarithmically completely monotonic functions are established.
Feng Qi,Xiao-Jing Zhang 대한수학회 2015 대한수학회보 Vol.52 No.3
In the paper, the authors discover an integral representation, some inequalities, and complete monotonicity of the Bernoulli numbers of the second kind.