Public key based key distribution scheme for wireless sensor networks by HUANG Jie1, HUANG Bei1

“…Since key pre-distribution schemes based on symmetric key can not completely solve security problems of keys distribution in WSN,a new public key based key distribution scheme was proposed.In the scheme,public key set was generated by an initial public key set and a hash function in base station.Each sensor device was pre-distributed one public/private pair-wise key from public key set and a public key subset from the initial public keys set.Owing to uniqueness of private key,not only the communication security problems could be improved for WSN.but also the sensor-memory cost could be decreased.With the theorem of random-graph theory,the connectivity and scalability were illustrated.The results showed that the scheme was superior to the traditional key pre-distribution schemes.…”
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Robust Asymptotical Stability and Stabilization of Fractional-Order Complex-Valued Neural Networks with Delay by Jingjing Zeng, Xujun Yang, Lu Wang, Xiaofeng Chen

“…It is worth noting that our system combines complex numbers, uncertain parameters, time delay, and fractional orders, which is universal in practical application. Using the theorem of homeomorphism, the sufficient condition of the existence and uniqueness of the equilibrium point for the system is obtained. …”
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Sequential Derivatives of Nonlinear q-Difference Equations with Three-Point q-Integral Boundary Conditions by Nittaya Pongarm, Suphawat Asawasamrit, Jessada Tariboon

“…By using Banach's contraction mapping, Krasnoselskii's fixed-point theorem, and Leray-Schauder degree theory, some new existence results are obtained. …”
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Synchronization of Chaotic Delayed Neural Networks via Impulsive Control by Yang Fang, Kang Yan, Kelin Li

“…By employing Lyapunov stability theorem, impulsive control theory and linear matrix inequality (LMI) technique, several new sufficient conditions ensuring the asymptotically synchronization for coupled chaotic delayed neural networks are derived. …”
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Reiterated homogenization of nonlinear monotone operators in a general deterministic setting by Dag Lukkassen, Gabriel Nguetseng, Hubert Nnang, Peter Wall

“…A general deterministic homogenization theorem is proved and several concrete examples are studied under various structure hypotheses ranging from the classical periodicity hypothesis to more complicated, but realistic, structure hypotheses.…”
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Solvability of a Second Order Nonlinear Neutral Delay Difference Equation by Zeqing Liu, Liangshi Zhao, Jeong Sheok Ume, Shin Min Kang

“…By means of the Krasnoselskii and Schauder fixed point theorem and some new techniques, we get the existence results of uncountably many bounded nonoscillatory, positive, and negative solutions for the equation, respectively. …”
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A Time Discontinuous Galerkin Finite Element Method for Quasi-Linear Sobolev Equations by Hong Yu, Tongjun Sun

“…The existence and uniqueness of the approximate solution are proved by use of Brouwer’s fixed point theorem. An optimal L∞(0,T;H1(Ω))-norm error estimate is derived. …”
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Restrictive metric regularity and generalized differential calculus in Banach spaces by Boris S. Mordukhovich, Bingwu Wang

“…Some sufficient as well as necessary and sufficient conditions for restrictive metric regularity are obtained, which particularly include an extension of the classical Lyusternik-Graves theorem in the case when f is strictly differentiable at x¯ but its strict derivative ∇f(x¯) is not surjective. …”
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Neural Sliding Mode Adaptive PD Tracking Control of Omnidirectional Mobile Robots by Zhang Kaiwen, Li Guoli, Xu Jiazi, Wang Qunjing, Wen Yan

“…Then, the neural network is used to approximate the uncertainty in the dynamics model, and the stability of the system is proved by the Lyapunov theorem. Simulation and experimental results show that the control strategy is effective.…”
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Stability and Bifurcation Analysis for a Delay Differential Equation of Hepatitis B Virus Infection by Xinchao Yang, Xiju Zong, Xingong Cheng, Zhenlai Han

“…The explicit formulae which determine the direction of the bifurcations, stability, and the other properties of the bifurcating periodic solutions are given by using the normal form theory and the center manifold theorem. Numerical simulation verifies the theoretical results.…”
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Properties of some ∗-dense-in-itself subsets by V. Renuka Devi, D. Sivaraj, T. Tamizh Chelvam

“…ℐ-open sets were introduced and studied by Janković and Hamlett (1990) to generalize the well-known Banach category theorem. Quasi-ℐ-openness was introduced and studied by Abd El-Monsef et al. (2000). …”
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Hopf Bifurcation Analysis of a Predator-Prey Biological Economic System with Nonselective Harvesting by Biwen Li, Zhenwei Li, Boshan Chen, Gan Wang

“…By using the local parameterization method and Hopf bifurcation theorem, we analyze the Hopf bifurcation of the proposed system. …”
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Dynamic Proportional Reinsurance and Approximations for Ruin Probabilities in the Two-Dimensional Compound Poisson Risk Model by Yan Li, Guoxin Liu

“…Via the Hamilton-Jacobi-Bellman approach we find a candidate for the optimal value function and prove the verification theorem. In addition, we obtain the Lundberg bounds and the Cramér-Lundberg approximation for the ruin probability and show that as the capital tends to infinity, the optimal strategies converge to the asymptotically optimal constant strategies. …”
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A New Approach to General Interpolation Formulae for Bivariate Interpolation by Le Zou, Shuo Tang

“…We discuss the interpolation theorem, algorithms, dual interpolation, and special cases and give many kinds of interpolation scheme. …”
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A New Hybrid Algorithm for a Pair of Quasi-𝜙-Asymptotically Nonexpansive Mappings and Generalized Mixed Equilibrium Problems in Banach Spaces by Jinhua Zhu, Shih-Sen Chang

“…Under suitable conditions some strong convergence theorems are established in a uniformly smooth and strictly convex Banach space with Kadec-Klee property. …”
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Iterative Algorithms for Solving the System of Mixed Equilibrium Problems, Fixed-Point Problems, and Variational Inclusions with Application to Minimization Problem by Tanom Chamnarnpan, Poom Kumam

“…Furthermore, we give a numerical example which supports our main theorem in the last part.…”
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Monotone and Concave Positive Solutions to a Boundary Value Problem for Higher-Order Fractional Differential Equation by Jinhua Wang, Hongjun Xiang, Yuling Zhao

“…By using fixed point theorem, we obtain some new results for the existence and multiplicity of solutions to a higher-order fractional boundary value problem. …”
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Existence of Homoclinic Orbits for a Singular Differential Equation Involving p-Laplacian by Honghui Yin, Bo Du, Qing Yang, Feng Duan

“…The approach is based on the continuation theorem for coincidence degree theory.…”
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Invariant Analysis, Analytical Solutions, and Conservation Laws for Two-Dimensional Time Fractional Fokker-Planck Equation by Nisrine Maarouf, Khalid Hilal

“…By using the new conservation theorem, the new conserved vectors for the two-dimensional time fractional Fokker-Planck equation have been constructed with a detailed derivation. …”
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Existence and Stability of Solutions for Hadamard-Stieltjes Fractional Integral Equations by Saïd Abbas, Eman Alaidarous, Mouffak Benchohra, Juan J. Nieto

“…We present two results: the first one is an existence result based on Schauder’s fixed point theorem and the second one is about the generalized Ulam-Hyers-Rassias stability.…”
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