The Largest Component of Near-Critical Random Intersection Graph with Tunable Clustering by Shiying Huang, Bin Wang

“…We prove that with high probability the size of the largest component in the weakly supercritical random intersection graph with tunable clustering on n vertices is of order nϵn, and it is of order ϵ−2nlognϵ3n in the weakly subcritical one, where ϵn⟶0 and n1/3ϵn⟶∞ as n⟶∞.…”
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Solution of Hamilton-Jacobi-Bellman Equation in Optimal Reinsurance Strategy under Dynamic VaR Constraint by Yuzhen Wen, Chuancun Yin

“…We obtain the closed form expression of the optimal reinsurance strategy and corresponding survival probability under proportional reinsurance.…”
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A Modified FNN Fault Diagnosis on PCVD Microwave System by Zhenyu Li, Hongsheng Li

“…The symptom variables are selected as the crisp inputs, and the corresponding membership functions are obtained from premeasured data as well as experts’ diagnostic experience/knowledge. The prior probability and the restriction coefficients are combined into the FNN algorithm via matrix operator. …”
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Analysis of Random Difference Equations Using the Differential Transformation Method by Şeyma Şişman, Mehmet Merdan

“…The expected value, variance, coefficient of variation, and confidence intervals of the solutions of random difference equations obtained from discrete probability distributions such as uniform, geometric, Poisson, and binomial distributions will be calculated. …”
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A New Proof of Central Limit Theorem for i.i.d. Random Variables by Zhaojun Zong, Feng Hu

“…Central limit theorem (CLT) has long and widely been known as a fundamental result in probability theory. In this note, we give a new proof of CLT for independent identically distributed (i.i.d.) random variables. …”
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BUILDING INFORMATION MODELING AS A TOOL FOR OPERATIONAL MANAGEMENT OF THE CONSTRUCTION PROCESS by A. Saitgaraev

“…Besides, the scheme of operational management of the course of construction process by means of BIM model which is the effective tool of the concept Lean Construction at the expense of what the probability of implementation of the project essentially increases in time is presented in article.…”
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Forecasting in Crisis Management Organization by V. N. Lokhanova

“…The list of critical indicators of the probability of bankruptcy.…”
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Increasing exposure of cotton growing areas to compound drought and heat events in a warming climate by Shengli Liu, Wei Zhang, Tongtong Shi, Tong Li, Hui Li, Guanyin Zhou, Zhanbiao Wang, Xiongfeng Ma

“…Furthermore, major cotton-producing countries exhibited similar CDHE trends, leading to a heightened probability of synchronous CDHE occurrences, except in countries connected to India and Pakistan. …”
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Studies on a Double Poisson-Geometric Insurance Risk Model with Interference by Yujuan Huang, Wenguang Yu

“…By martingale and stopping time approach, we obtain adjustment coefficient equation, the Lundberg inequality, and the formula for the ruin probability. Also the Laplace transformation of the time when the surplus reaches a given level for the first time is discussed, and the expectation and its variance are obtained. …”
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On the birthday problem: some generalizations and applications by P. N. Rathie, P. Zörnig

“…We discuss the unimodality of the corresponding exact probability distribution and express the moments and generating functions by means of confluent hypergeometric functions U(−;−;−) which are computable using the software Mathematica. …”
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Prehospital Use of the Intubating Laryngeal Mask Airway in Patients with Severe Polytrauma: A Case Series by Andrew M. Mason

“…All patients were hypoxaemic, had sustained severe polytrauma and were trapped in their vehicles following road traffic collisions. A probability of survival study showed better-than-predicted outcomes for the group as a whole.…”
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A Note on Impulsive Fractional Evolution Equations with Nondense Domain by Zufeng Zhang, Bin Liu

“…Some errors in the existing paper concerned with nondensely defined fractional differential equations are pointed out, and correct formula of integral solutions is established by using integrated semigroup and some probability densities. Sufficient conditions for the existence are obtained by applying the Banach contraction mapping principle. …”
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Stability of a Three-Species Cooperative System with Time Delays and Stochastic Perturbations by Jinxing Zhao, Yuanfu Shao

“…We establish the sufficient criteria of the asymptotical stability and stability in probability by constructing a neutral stochastic differential equation and some suitable functionals. …”
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The Effect of a Service Experience Cost on a Queueing System by Xuelu Zhang, Qing Ma

“…The SE cost decreases the equilibrium joining probability and social welfare in an unobservable case. …”
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Phase Transition in Long-Range Percolation on Bipartite Hierarchical Lattices by Yilun Shang

“…We study long-range percolation on the bipartite hierarchical lattice where any edge (running between vertices of unlike bipartition sets) of length k is present with probability , independently of all other edges. The parameter is the percolation parameter, while describes the long-range nature of the model. …”
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Numerical Solutions of Stochastic Differential Delay Equations with Poisson Random Measure under the Generalized Khasminskii-Type Conditions by Minghui Song, Hui Yu

“…The main aims of this paper are to prove the existence of global solutions to such equations and then to investigate the convergence of the Euler method in probability under the generalized Khasminskii-type conditions. …”
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Dynamics of Stochastic Coral Reefs Model with Multiplicative Nonlinear Noise by Zaitang Huang

“…Meanwhile, the density of the distribution of the solutions either converges to a stationary density or weakly converges to some probability measure.…”
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Approximate Solutions of Hybrid Stochastic Pantograph Equations with Levy Jumps by Wei Mao, Xuerong Mao

“…We prove that the approximate solutions converge to the true solutions in sense as well as in probability under local Lipschitz condition and generalize the results obtained by Fan et al. (2007), Milošević and Jovanović (2011), and Marion et al. (2002) to cover a class of more general stochastic pantograph differential equations with jumps. …”
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A Note on the Tail Behavior of Randomly Weighted Sums with Convolution-Equivalently Distributed Random Variables by Yang Yang, Jun-feng Liu, Yu-lin Zhang

“…Our obtained result can be directly applied to a discrete-time insurance risk model with insurance and financial risks and derive the asymptotics for the finite-time probability of the above risk model.…”
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An Extension of a result of Csiszar by P. B. Cerrito

“…If α=1, we show that there exists a sequence of elements {an} In S such that μn∗δan converges vaguely to a probability measure where δ denotes point mass. In particular, we apply the results to inverse and matrix semigroups.…”
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