The Stochastic Θ-Method for Nonlinear Stochastic Volterra Integro-Differential Equations by Peng Hu, Chengming Huang

“…Then, a sufficient condition for mean-square exponential stability of the true solution is given. …”
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Eigenvalue Based Approach for Global Consensus in Multiagent Systems with Nonlinear Dynamics by Wei Qian, Lei Wang

“…By employing a Lyapunov function and graph theory, a sufficient condition is presented for the global exponential consensus of the multiagent system. The analytical result shows that, for a weakly connected communication graph, the algebraic connectivity of a redefined symmetric matrix associated with the directed graph is used to evaluate the global consensus of the multiagent system with nonlinear dynamics under the common linear consensus protocol. …”
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General Recurrent Neural Network for Solving Generalized Linear Matrix Equation by Zhan Li, Hong Cheng, Hongliang Guo

“…If the linear activation function is utilized, the neural state matrix of the nonlinear recurrent neural network can globally and exponentially converge to the unique theoretical solution of GLME. …”
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Cyberattack on the National Health Laboratory Service of South Africa – implications, response and recommendations by S Cassim, Z C Chapanduka

“…Cyberattacks primarily targeting healthcare institutions have increased exponentially. Recently, the information technology systems of the National Health Laboratory Service (NHLS) of South Africa (SA) were targeted by cyberterrorists using disruptive ransomware. …”
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A series transformation formula and related polynomials by Khristo N. Boyadzhiev

“…In one particular case, our formula reduces to a series transformation formula which appears in the works of Ramanujan and is related to the exponential (or Bell) polynomials. Another particular case, based on the geometric series, gives rise to a new class of polynomials called geometric polynomials.…”
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Preliminary study on the connotation of flexibility in dynamically reconfigurable networks by Dong-nian CHENG, Bin-qiang WANG, Bao-jin WANG, Jian-hui ZHANG

“…,the dynamic data channel varying with service demands,of reconfigurable networks was first exhibited and explained.Four dominant implications of the flexibility were then revealed as gradually mapping to demands,keeping global performance good,implicit isolation,and self-driven control.Finally,related quantitative models and methods for both determining the stable deviation of outcomes from demands and computing the volume of resource dynamically reconfigured were investigated by using the exponentially moving average,the n:m voting scheme,Markov decision processes (MDP) and reinforcement learning,respectively.…”
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Structural properties and static robustness of Linux software network by Ershen WANG, Yu LI, Chen HONG, Qinghua SUN, Chang LIU

“…The source code of the Linux software was analyzed,and the directed function call network model,the weak coupling network model of software system,the strong coupling network model and the strong connected subgraph model were built.The characteristics and static robustness of the four networks were studied.The results show that four networks all show ‘small-world’ property.The out-degree distribution of the six modules in the Linux network generally follows the exponential distribution,and the in-degree distribution of the six modules follows the power law.The best attacking strategy was distinct when different robustness evaluation indicator was adopted.For the weak connectivity indicator,high in-degree attacking strategy was of the greatest damage to the weakly coupled software network.…”
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Thermalization in Krylov basis by Mohsen Alishahiha, Mohammad Javad Vasli

“…We demonstrate that for thermalization to occur, the matrix representation of typical local operators in the Krylov basis should exhibit a specific tridiagonal form with all other elements in the matrix being exponentially small, reminiscent of the eigenstate thermalization hypothesis. …”
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Fast Fourier Transform Based Power Option Pricing with Stochastic Interest Rate, Volatility, and Jump Intensity by Jiexiang Huang, Wenli Zhu, Xinfeng Ruan

“…Firstly, we present a more general and realistic double-exponential jump model with stochastic volatility, interest rate, and jump intensity. …”
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A Simple Repairable System with Warning Device by Xiao Zhang, Lina Guo

“…Then the unique existence and asymptotic stability, especially the exponential stability of the system dynamic solution, are studied by using the strongly continuous semigroup theory or C0 semigroup theory and the spectrum theory. …”
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Gamma Splines and Wavelets by Hannu Olkkonen, Juuso T. Olkkonen

“…The gamma splines are born by -times convolution of the exponential by itself. We study the properties of the discrete gamma splines in signal interpolation and approximation. …”
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Tanatopolítica y control social : la violencia como dinamizador del orden y la limpieza social en Bucaramanga, Colombia (1988-1998) by Álvaro Acevedo Tarazona, Andrés Correa Lugos

“…At the end of the 20th century, Colombia saw an exponential growth in violence as a result of the boom in drug trafficking and the internal armed conflict. …”
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Using Time-Space Double Radial Basis Function Method to Solve High-Dimensional PDEs Arising from Multiasset Option Pricing by Zhiqiang Zhou, Hongying Wu, Caijuan Kang, You Wu

“…Numerical examples confirm that the TSDRBF method has exponentially convergent rates for the number N and number M, while the convergence is linear for the number M¯. …”
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Deep First Formal Concept Search by Tao Zhang, Hui Li, Wenxue Hong, Xiamei Yuan, Xinyu Wei

“…The calculation of formal concepts is a very important part in the theory of formal concept analysis (FCA); however, within the framework of FCA, computing all formal concepts is the main challenge because of its exponential complexity and difficulty in visualizing the calculating process. …”
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Fréchet Random Noise for k-Regime-Switching Mixture Autoregressive Model by Rasaki, Olawale Olanrewaju, Anthony, Gichuhi Waititu, Nafiu, Lukman Abiodun

“…The limiting distribution of the FMAR(k; p1, p2 ,, pk ) model via Gnedenko-Fisher Tippet limiting property was derived to asymptotically approach an exponential function.…”
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The Future of Harmful Algal Blooms in Florida Inland and Coastal Waters by Karl Havens

“…Warmer water temperatures and increased nutrient levels exacerbate blooms, and when nutrients are high, temperature increases of just a few degrees cause exponential increases of algae and blooms. This 4-page fact sheet written by Karl Havens and published by the Florida Sea Grant College Program and UF/IFAS Extension explains why algal blooms can be harmful and provides advice for communities seeking to reduce nutrient levels in their lakes, streams, and other bodies of water. …”
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The Future of Harmful Algal Blooms in Florida Inland and Coastal Waters by Karl Havens

“…Warmer water temperatures and increased nutrient levels exacerbate blooms, and when nutrients are high, temperature increases of just a few degrees cause exponential increases of algae and blooms. This 4-page fact sheet written by Karl Havens and published by the Florida Sea Grant College Program and UF/IFAS Extension explains why algal blooms can be harmful and provides advice for communities seeking to reduce nutrient levels in their lakes, streams, and other bodies of water. …”
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DNA algorithm of primeness test based on finite automaton by YANG Xue-qing, LIU Zhong-kan

“…Finite automaton,a computational model of extremely limited computing ability,was proved to have the capa-bility of solving primeness test by construction.Then,a DNA algorithm of the primeness test based on finite automaton was proposed.Furthermore,the method of constructing the finite automaton was presented in detail.The state of the fi-nite automaton was encoded by single-stranded DNA.The input was encoded by double-stranded DNA.The transition rule was represented by a double strand with a ring.The state of transition was realized by enzyme-mediated chemical reactions.The innovation of the algorithm is that it can be applied not only in primeness test but also in prime factoriza-tion and further in attack of RSA cipher.The advantage of this method is that it can be easily implemented.The time re-quired is polynomial in the size of the problem instead of exponential in the size of the problem.…”
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Convergence Rate Estimate of Distributed Localization Algorithms in Wireless Sensor Networks by Shujuan Pang

“…In this paper, we mainly show that for the consistent case the convergence rate of the optimal consensus will be exponential under some basic conditions, while for the inconsistent case we provide a necessary condition for the optimal consensus and a convergence rate estimate inequality. …”
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Impacts of coal fracture roughness and aperture on the seepage of injected water: An experimental study by Gang WANG, Xuechang CHEN, Hao CHEN, Qingming LONG, Yixin LIU

“…The seepage rate of coals increased exponentially with an increase in the fracture aperture. …”
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