Refinements of Various Types of Fractional Inequalities via Generalized Convexity by Yong Tang, Ghulam Farid, M. Y. Youssif, Zakieldeen Aboabuda, Amna E. Elhag, Kahkashan Mahreen

“…This paper aims to find generalizations of inequalities that hold for unified integral operators by applying strongly exponentially α,ℏ−m−p-convex functions. These inequalities generate results for several fractional integral operators and simultaneously hold for convex, strongly convex, and exponentially convex functions. …”
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Stability Analysis of Stochastic Reaction-Diffusion Cohen-Grossberg Neural Networks with Time-Varying Delays by Chuangxia Huang, Xinsong Yang, Yigang He

“…This paper is concerned with pth moment exponential stability of stochastic reaction-diffusion Cohen-Grossberg neural networks with time-varying delays. …”
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Modelling and analysis of coalbed methane drainage quality in penetrating-strata boreholes considering air leakage by Lizhen Zhao, Tianxuan Hao, Dengke Wang, Jianping Wei, Yang Du, Baisheng Nie, Jie Chen, Zhen Li, Yiju Tang, Fukai Zhang, Bowen Dong, Yuling Xia

“…The CBM drainage quality exponentially increases with Langmuir content and exponentially decreases with Langmuir pressure. …”
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A New Precursor Integral Method for Solving Space-Dependent Kinetic Equations in Neutronic and Thermal-Hydraulic Coupling System by Yingjie Wu, Baokun Liu, Han Zhang, Jiong Guo, Fu Li, Jinlin Niu, Yizhen Wang, Menglei Cui

“…The truncation errors of exponential approximation and Taylor approximation are analyzed and compared. …”
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The Jump Size Distribution of the Commodity Spot Price and Its Effect on Futures and Option Prices by L. Gómez-Valle, Z. Habibilashkary, J. Martínez-Rodríguez

“…Moreover, the Exponential distribution provides the highest premia in absolute value.…”
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Global Stability of Almost Periodic Solution of a Class of Neutral-Type BAM Neural Networks by Tetie Pan, Bao Shi, Jian Yuan

“…By employing fixed-point theorem, the exponential dichotomy, and differential inequality techniques, we obtain some sufficient conditions to insure the existence and globally exponential stability of almost periodic solution. …”
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Introducing Randomness into First-Order and Second-Order Deterministic Differential Equations by John F. Moxnes, Kjell Hausken

“…Analytical results are presented for a deterministic linear friction force and a stochastic force that is uncorrelated or exponentially correlated.…”
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Some Generalized Formulas of Hadamard-Type Fractional Integral Inequalities by Xiujun Zhang, Ghulam Farid, Hafsa Yasmeen, Kamsing Nonlaopon

“…This paper is aimed at establishing the generalized forms of Riemann-Liouville fractional inequalities of the Hadamard type for a class of functions known as strongly exponentially α,h−m-p-convex functions. These inequalities provide some general formulas from which one can get associated inequalities for various types of exponentially convex and strongly convex functions. …”
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Distribution Pattern of Anchorage Stress and Water Sensitivity Analysis of Red Clay by Lifeng Li, Weili Gong, Huilin Deng, Xiaohu Zhang, Gan Li

“…With increasing anchorage force, the dynamic evolution (single exponential distribution ⟶ double single exponential distribution ⟶ uniform index exponential complex distribution ⟶ uniform distribution) of the anchorage shear stress is analysed. …”
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Stability of Stochastic Reaction-Diffusion Recurrent Neural Networks with Unbounded Distributed Delays by Chuangxia Huang, Xinsong Yang, Yigang He, Lehua Huang

“…Some new sufficient conditions to guarantee the almost sure exponential stability and mean square exponential stability of an equilibrium solution are obtained, respectively. …”
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Practical Stability for Conformable Time-Delay Systems by Maher Kharrat, Hamdi Gassara, Mohamed Rhaima, Lassaad Mchiri, A. Ben Makhlouf

“…This article investigates the practical exponential stability and design problems of conformable time-delay systems. …”
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Generalizations of Parisi’s replica symmetry breaking and overlaps in random energy models by Derrida, Bernard, Mottishaw, Peter

“…All these statistical properties can be understood by considering that the low energy levels are the points generated by a Poisson process with an exponential density. Here we first show how, by replacing the exponential density by a sum of two exponentials, the overlaps statistics are modified. …”
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The Dependency of Diffusion Coefficients and Geometric Factor on the Size of the Diffusing Molecule: Observations for Different Clay-Based Materials by Elke Jacops, Marc Aertsens, Norbert Maes, Christophe Bruggeman, Rudy Swennen, Bernd Krooss, Alexandra Amann-Hildenbrand, Ralf Littke

“…We observed that, for unreactive gases in clayey materials, the effective diffusion coefficient varies with the size of the diffusing molecule and this variation can be described by an exponential or a power law function. The variation of the geometric factor can also be described by an exponential function. …”
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Dynamics of Fuzzy BAM Neural Networks with Distributed Delays and Diffusion by Qianhong Zhang, Lihui Yang, Jingzhong Liu

“…Constructing a new Lyapunov functional and employing inequality technique, the existence, uniqueness, and global exponential stability of the periodic oscillatory solution are investigated for a class of fuzzy bidirectional associative memory (BAM) neural networks with distributed delays and diffusion. …”
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Stability Analysis and Robust H∞ Control of Switched Stochastic Systems with Time-Varying Delay by Zhengrong Xiang, Guoxin Chen

“…The problems of mean-square exponential stability and robust H∞ control of switched stochastic systems with time-varying delay are investigated in this paper. …”
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Spatial behavior for the quasi-static heat conduction within the second gradient of type Ⅲ by Jincheng Shi, Shuman Li, Cuntao Xiao, Yan Liu

“…When the distance tends to infinity, the energy either grows exponentially or decays exponentially. The results showed that the Saint-Venant principle was also valid for the quasi-static biharmonic conduction equation.…”
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On Solvability of Third-Order Operator Differential Equation with Parabolic Principal Part in Weighted Space by Araz R. Aliev, Sabir S. Mirzoev, Mustafa A. Soylemezo

“…Besides, the connection is found between the order of exponential weight and the lower bound for the spectrum of abstract operator appearing in the principal part of the equation.…”
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Parametric Instabilities in Time-Varying Compressible Linear Flows by Ioannis Kiorpelidis, Nikolaos A. Bakas

“…Elliptical instability occurs because the scale of the acoustic waves decreases exponentially and their wave action is conserved, leading to an exponential increase in the acoustic waves’ energies. …”
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A Study of the Source Traffic Generator Using Poisson Distribution for ABR Service by Mohsen Hosamo

“…This traffic generator inherits the advantages of both Poisson and exponential distribution functions to achieve enhanced link performance. …”
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Fitting of nonnegative physical models based on statistical divergence: application to thermally stimulated depolarization currents by Yasunobu Ando, Shusuke Kasamatsu, Suguru Iwasaki, Yumi Tanaka

“…To demonstrate this formalism, parameters were estimated in a theoretical model of the thermally stimulated depolarisation current (TSDC), which has a non-negative but complex exponential form. Some technical aspects were also discussed as key points to enable high-throughput fitting of multimode models of TSDC using the proposed formalism, such as the use of the peak temperature as a fitting parameter, which is easily estimated from measured data, instead of a pre-exponential factor that varies by orders of magnitude, and the use of the generalised exponential integral function to speed up the fitting algorithm.…”
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