Existence of Generalized Homoclinic Solutions of Lotka-Volterra System under a Small Perturbation by Yuzhen Mi

“…By the Fourier series expansion technique method, the fixed point theorem, the perturbation theorem, and the reversibility, we prove that near μ=0 the system has a generalized homoclinic solution exponentially approaching a periodic solution.…”
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A Theory of Summability on a Space of Generalized Functions by Khaula Naeem Khan, Wilson Lamb

“…A space of almost-periodic generalized functions, in which each generalized function can be expanded in terms of an uncountable basis of exponential functions, is obtained as a special case of our theory.…”
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Stability Analysis of Predator-Prey System with Fuzzy Impulsive Control by Yuangan Wang

“…Via the T-S model and the Lyapunov method, the controlling conditions of the asymptotical stability and exponential stability are established. Furthermore, the numerical simulation for the Lotka-Volterra predator-prey system with impulsive effects verifies the effectiveness of the proposed methods.…”
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Searching for Analytical Solutions of the (2+1)-Dimensional KP Equation by Two Different Systematic Methods by Yongyi Gu, Fanning Meng

“…Using the exp⁡(-ψ(z))-expansion method, exact solutions of the mentioned equation including hyperbolic, exponential, trigonometric, and rational function solutions have been obtained. …”
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Gambling minds: what lies behind the BETS? by César Augusto Trinta Weber, Antonio Geraldo da Silva

“…Online sports betting, known as bets, has gained exponential popularity, posing significant public health challenges. …”
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Some New Generalized Fractional Newton’s Type Inequalities for Convex Functions by Jarunee Soontharanon, Muhammad Aamir Ali, Hüseyin Budak, Pinar Kösem, Kamsing Nonlaopon, Thanin Sitthiwirattham

“…The main edge of the newly established inequalities is that these can be turned into several new and existing inequalities for different fractional integrals like Riemann-Liouville fractional integrals, k-fractional integrals, Katugampola fractional operators, conformable fractional operators, Hadamard fractional operators, and fractional operators with the exponential kernel without proving one by one. It is also shown that the newly established inequalities are the refinements of the previously established inequalities inside the literature.…”
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Photoproducts Formation from Salicylic Acid and Poly(allylamine hydrochloride) in Aqueous Solution Induced by UV-B Radiation by Romario J. da Silva, Nara C. de Souza, Josmary R. Silva

“…These processes were well fitted with first-order exponential functions.…”
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Vulnerability Analysis of Power Grids Using Modified Centrality Measures by Francisco Gutierrez, E. Barocio, F. Uribe, P. Zuniga

“…To support the idea of using modified centralities, four power grids are tested to be either exponential or scale-free. To evaluate the proposal, information obtained via modified centrality measures is used to calculate global efficiency of the power grids.…”
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Stability Analysis and Design of Time-Varying Nonlinear Systems Based on Impulsive Fuzzy Model by Yuangan Wang, Honglin Yu, Xiaohong Zhang, Dong Li

“…Several criteria on general stability, asymptotic stability, and exponential stability are established, and a simple design algorithm is provided with stability of nonlinear time-invariant systems. …”
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Weighted Pseudo Almost-Periodic Functions and Applications to Semilinear Evolution Equations by Jun Zhang, Ti-Jun Xiao, Jin Liang

“…Moreover, we prove an existence theorem for the weighted pseudo almost-periodic mild solution to the semilinear evolution equation: x′(t)=Ax(t)+f(t,x(t)), t∈ℝ, where A is the infinitesimal generator of an exponentially stable C0-semigroup. An application is also given to illustrate the abstract existence theorem.…”
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Numerical Algorithm Based on Haar-Sinc Collocation Method for Solving the Hyperbolic PDEs by A. Pirkhedri, H. H. S. Javadi, H. R. Navidi

“…The advantages of this technique are that not only is the convergence rate of Sinc approximation exponential but the computational speed also is high due to the use of the Haar operational matrices. …”
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Bounds for the mean square error of reliability estimation from gamma distribution in presence of an outlier observation by M. E. Ghitany, W. H. Laverty

“…A semi-Bayesian approach is discussed when the outlier effect on σ is treated as a random variable having a prior distribution of beta type. Results of the exponential distribution (Sinha [1]) are given as particular cases of our results.…”
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Event-Based State Estimation for Networked Singularly Perturbed Complex Networks by Zerong Ren

“…Depending on the singularly-perturbed-based Lyapunov theory, a sufficient condition is constructed to guarantee that the estimation error is exponentially ultimately bounded in the mean square. …”
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Variants of the Sliding Mode Control in Presence of External Disturbance for Quadrotor by Irfan Ahmad, Muwaida Liaquat, Fahad Mumtaz Malik, Hameed Ullah, Usman Ali

“…In this paper, an Improved Integral Power Rate Exponential Reaching Law (IIPRERL) Sliding Mode Control strategy has been presented to cater to the chattering problem and stability issue with the focusing on to achieve minimum steady-state errors in the presence of matched disturbances for a quadrotor. …”
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RELIABILITY ASSESSMENT MODEL BASED ON RELATIVE ENTROPY INFORMATION FUSION WITH DOUBLE CONSTANT ACCELERATING STRESSES by YIN ZeKai, TANG JiaYin, HE Ping

“…The comprehensive reliability evaluation model,fusing exponential and Weibull natural storage field data and accelerated storage sample data,was built based on the integrating of relative entropy and the least square method. …”
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Mean-periodic functions by Carlos A. Berenstein, B. A. Taylor

“…We show that any mean-periodic function f can be represented in terms of exponential-polynomial solutions of the same convolution equation f satisfies, i.e., u∗f=0(μ∈E′(ℝn)). …”
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Truncated Cauchy Power Odd Fréchet-G Family of Distributions: Theory and Applications by M. Shrahili, I. Elbatal

“…Two real-world datasets are used to show the importance and flexibility of the new family by using the truncated Cauchy power odd Fréchet exponential model as example of the family and compare it with some known models, and this model proves the importance and the flexibility for the new family.…”
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A Class of Approximate Damped Oscillatory Solutions to Compound KdV-Burgers-Type Equation with Nonlinear Terms of Any Order: Preliminary Results by Yan Zhao, Weiguo Zhang

“…The results indicate that errors between implicit exact damped oscillatory solutions and approximate damped oscillatory solutions are infinitesimal decreasing in the exponential form.…”
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On the Existence and Robustness of Steady Position-Momentum Correlations for Time-Dependent Quadratic Systems by M. Gianfreda, G. Landolfi

“…In particular, steady statistical momentum averages are seen over well-defined time intervals in the evolution of a linear superposition of the basis states of modified exponentially damped mass systems.…”
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On the reflection of Alfvén waves in an ideal magnetoatmosphere by Hadi Yahya Alkahby, M. A. Mahrous

“…Below the critical layer, the solution of the problem can be written as a linear combination of an upward and a downward propagating wave and above it the solution decays exponentially with the altitude. The location of the critical layer and the magnitude of the reflection coefficient are determined and the conclusions are discussed in cormeetion with the heating mechanism of the solar atmosphere…”
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