In this paper we show that a log-convex function satisfies Hadamard's inequality, as well as we give an extension for this result in several directions.
Extensions of the Gordon-Loeb [1] and the Gordon-Loeb-Lucyshyn-Zhou [2] models are presented based on mathematical equivalency with a generalized homeland security model. The extensions include limitations on changes ...Extensions of the Gordon-Loeb [1] and the Gordon-Loeb-Lucyshyn-Zhou [2] models are presented based on mathematical equivalency with a generalized homeland security model. The extensions include limitations on changes in the probability of attack, simultaneous effects on probability and loss, diversion of attack, and shared non-information defenses. Legal cases are then investigated to assess approximate magnitudes of external effects and the extent they are internalized by the legal system.展开更多
This article proposes a method for fitting models subject to a convex and log-convex constraint on the probability vector of a product multinomial （binomial） distribution. We present an iterative algorithm for findi...This article proposes a method for fitting models subject to a convex and log-convex constraint on the probability vector of a product multinomial （binomial） distribution. We present an iterative algorithm for finding the restricted maximum likelihood estimates （MLEs） of the probability vector and show that the algorithm converges to the true solution. Some examples are discussed to illustrate the method.展开更多
In 2012,Zhi-Wei Sun posed many conjectures about the monotonicity of sequences of form {n√zn},where {zn} is a familiar number-theoretic or combinatorial sequence. We show that if the sequence {zn+1/zn}is increasing(r...In 2012,Zhi-Wei Sun posed many conjectures about the monotonicity of sequences of form {n√zn},where {zn} is a familiar number-theoretic or combinatorial sequence. We show that if the sequence {zn+1/zn}is increasing(resp.,decreasing),then the sequence {n√zn} is strictly increasing(resp.,decreasing) subject to a certain initial condition. We also give some sufficient conditions when {zn+1/zn} is increasing,which is equivalent to the log-convexity of {zn}. As consequences,a series of conjectures of Zhi-Wei Sun are verified in a unified approach.展开更多
This paper studies the complete monotonicity of the probability of ruin in the the classical risk model and the classical risk model that is perturbed by a diffusion. As a byproduct, the authors give an alternative p...This paper studies the complete monotonicity of the probability of ruin in the the classical risk model and the classical risk model that is perturbed by a diffusion. As a byproduct, the authors give an alternative proof to a result on the optimal dividend problem due to Loeffen （2008）.展开更多
Two interesting sequences arose in the study of the series expansions of the complete elliptic integrals,which are called the Catalan-Larcombe-French sequence{Pn}n≥0 and the Fennessey-Larcombe-French sequence{Vn}n≥0...Two interesting sequences arose in the study of the series expansions of the complete elliptic integrals,which are called the Catalan-Larcombe-French sequence{Pn}n≥0 and the Fennessey-Larcombe-French sequence{Vn}n≥0 respectively.In this paper,we first establish some criteria for determining log-behavior of a sequence based on its three-term recurrence.Then we prove the log-convexity of{Vn^2-V(n-1)V(n+1)}n≥2 and{n!Vn}n≥1,the ratio log-concavity of{Pn}n≥0 and the sequence{An}n≥0 of Apéry numbers,and the ratio log-convexity of{Vn}n≥1.展开更多
文摘In this paper we show that a log-convex function satisfies Hadamard's inequality, as well as we give an extension for this result in several directions.
文摘Extensions of the Gordon-Loeb [1] and the Gordon-Loeb-Lucyshyn-Zhou [2] models are presented based on mathematical equivalency with a generalized homeland security model. The extensions include limitations on changes in the probability of attack, simultaneous effects on probability and loss, diversion of attack, and shared non-information defenses. Legal cases are then investigated to assess approximate magnitudes of external effects and the extent they are internalized by the legal system.
基金Supported by the National Natural Science Foundation of China(No.11071008)Scientific Foundations of Beijing Jiaotong University(No.2012JBM105)
文摘This article proposes a method for fitting models subject to a convex and log-convex constraint on the probability vector of a product multinomial （binomial） distribution. We present an iterative algorithm for finding the restricted maximum likelihood estimates （MLEs） of the probability vector and show that the algorithm converges to the true solution. Some examples are discussed to illustrate the method.
基金supported by National Natural Science Foundation of China(Grant Nos.11071030,11201191 and 11371078)Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20110041110039)+1 种基金National Science Foundation of Jiangsu Higher Education Institutions(GrantNo.12KJB110005)the Priority Academic Program Development of Jiangsu Higher Education Institutions(Grant No.11XLR30)
文摘In 2012,Zhi-Wei Sun posed many conjectures about the monotonicity of sequences of form {n√zn},where {zn} is a familiar number-theoretic or combinatorial sequence. We show that if the sequence {zn+1/zn}is increasing(resp.,decreasing),then the sequence {n√zn} is strictly increasing(resp.,decreasing) subject to a certain initial condition. We also give some sufficient conditions when {zn+1/zn} is increasing,which is equivalent to the log-convexity of {zn}. As consequences,a series of conjectures of Zhi-Wei Sun are verified in a unified approach.
基金supported by the National Natural Science Foundation of China under Grant No.11171179the Research Fund for the Doctoral Program of Higher Education of China under Grant No.20093705110002
文摘This paper studies the complete monotonicity of the probability of ruin in the the classical risk model and the classical risk model that is perturbed by a diffusion. As a byproduct, the authors give an alternative proof to a result on the optimal dividend problem due to Loeffen （2008）.
基金partially supported by the National Science Foundation of Xinjiang Uygur Autonomous Region(No. 2017D01C084)the National Science Foundation of China (Nos. 11771330 and 11701491)
文摘Two interesting sequences arose in the study of the series expansions of the complete elliptic integrals,which are called the Catalan-Larcombe-French sequence{Pn}n≥0 and the Fennessey-Larcombe-French sequence{Vn}n≥0 respectively.In this paper,we first establish some criteria for determining log-behavior of a sequence based on its three-term recurrence.Then we prove the log-convexity of{Vn^2-V(n-1)V(n+1)}n≥2 and{n!Vn}n≥1,the ratio log-concavity of{Pn}n≥0 and the sequence{An}n≥0 of Apéry numbers,and the ratio log-convexity of{Vn}n≥1.
