Analytical Techniques for a Numerical Solution of the Linear Volterra Integral Equation of the Second Kind by M. I. Berenguer, D. Gámez, A. I. Garralda-Guillem, M. Ruiz Galán, M. C. Serrano Pérez

“…In this work we use analytical tools—Schauder bases and Geometric Series theorem—in order to develop a new method for the numerical resolution of the linear Volterra integral equation of the second kind.…”
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The product of r−k and ∇δ on ℝm by C. K. Li

“…The nice properties of the δ-sequence are fully shown and used in the proof of our theorem.…”
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On Parametric Gevrey Asymptotics for Some Cauchy Problems in Quasiperiodic Function Spaces by A. Lastra, S. Malek

“…Our result rests on the classical Ramis-Sibuya theorem which asks to prove that the difference of any two neighboring constructed solutions satisfies some exponential decay. …”
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Physical layer security of relay selection NOMA wireless systems by LUO Yancui, LI Guangqiu, YE Mingzhu, GAO Hui, ZHANG Yajuan

“…The approximate expressions of secrecy outage probability(SOP) and asymptotic SOP of multi-relay selection MF-NOMA wireless systems with non-colluding or colluding eavesdropping scenarios were derived by using Gauss-Chebyshev Quadrature theorem. The simulation results verify the accuracy of PLS performance analysis of the above MF-NOMA wireless systems. …”
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On Existence of Multiplicity of Weak Solutions for a New Class of Nonlinear Fractional Boundary Value Systems via Variational Approach by Fares Kamache, Salah Mahmoud Boulaaras, Rafik Guefaifia, Nguyen Thanh Chung, Bahri Belkacem Cherif, Mohamed Abdalla

“…More precisely, we establish the existence of at least three weak solutions for the problem using variational methods combined with the critical point theorem due to Bonano and Marano. In addition, some examples in ℝ3 and ℝ4 are given to illustrate the theoritical results.…”
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The Results on the Existence of Fixed Points in Hilbert Spaces via Functions of Class $C$ by Mana Donganont, Arsalan Ansari, Snjezana Maksimovic, Zoran Mitrovic

“…Recently, Chouhan and Desai published a paper [Some Common Fixed-Point Theorems in Hilbert Space, J. Eemerg. Technol. Innov. …”
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Dynamic Behaviors of a Discrete Lotka-Volterra Competition System with Infinite Delays and Single Feedback Control by Liang Zhao, Xiangdong Xie, Liya Yang, Fengde Chen

“…By applying the discrete comparison theorem, a set of sufficient conditions which guarantee the permanence of the system is obtained. …”
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Joint DFT and Spacetime Coding for MU-OFDM in Power-Constrained Optical Wireless Communication Systems by Dianbin Lian, Yan Gao, Jie Lian, Yong Li

“…In our study, we introduce the weighted Bussgang theorem as an alternative method for evaluating the communication performance of hard-clipped systems due to the transmitted power constraint. …”
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Convergence criteria of branched continued fractions by I.B. Bilanyk, D.I. Bodnar, O.G. Vozniak

“…A multidimensional generalization of Worpitzky's and van Vleck's convergence theorems, the Śleszyński-Pringsheim theorem for the considered types of branched continued fractions are considered. …”
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Novel Design of High-Gain Planar Dipole-Array Antenna for RFID 2.45 GHz by Danpeng Xie, Xueguan Liu, Huiping Guo, Xinmi Yang

“…The radiation pattern of the array is discussed according to Arrays Theorem. The measured −10 dB band is from 2.3 GHz to 2.57 GHz, and peak gain in this band is 7.5 dBi. …”
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Polynomials in Control Theory Parametrized by Their Roots by Baltazar Aguirre-Hernández, José Luis Cisneros-Molina, Martín-Eduardo Frías-Armenta

“…Additionally we obtain a Boundary Theorem.…”
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Mathematical Model of Pipeline Abandonment and Recovery in Deepwater by Xia-Guang Zeng, Meng-Lan Duan, Chen An

“…Finally, an approximate formula for quick calculation of the suspended pipeline length is proposed based on Buckingham’s Pi-theorem and mathematical fitting.…”
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Stability Analysis of a Fractional-Order SEIR-KS Computer Virus-Spreading Model with Two Delays by Zhufeng Wang, Xiaoqian Nie, Maoxin Liao

“…The sufficient conditions for solving the stability and the occurrence of Hopf bifurcation of the system are established by using Laplace transform, stability theory, and Hopf bifurcation theorem of fractional-order differential systems. …”
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On the convergence of Fourier series by Geraldo Soares de Souza

“…Bp is continuously contained in Lp for 1≤p<∞, but different. We have THEOREM. Let 1<p<∞. If f∈Bp then the maximal operator Tf(x)=supn|Sn(f,x)| maps Bp into the Lorentz space L(p,1) boundedly, where Sn(f,x) is the nth-sum of the Fourier Series of f.…”
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Existence of Some Semilinear Nonlocal Functional Differential Equations of Neutral Type by Hsiang Liu, Cheng-Wen Liao, Chin-Tzong Pang

“…We first employ the Schauder fixed-point theorem to prove the existence of solution on the interval for that is small enough, and, then, by letting and using a diagonal argument, we have the existence results on the interval . …”
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Nearly Quadratic n-Derivations on Non-Archimedean Banach Algebras by Madjid Eshaghi Gordji, Badrkhan Alizadeh, Young Whan Lee, Gwang Hui Kim

“…We investigate the Hyers-Ulam stability of quadratic n-derivations from non-Archimedean Banach algebras into non-Archimedean Banach modules by using the Banach fixed point theorem.…”
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An Improved Nonhomogeneous Grey Model with Fractional-Order Accumulation and Its Application by Shuanghua Liu, Qin Qi, Zhiming Hu

“…For this, this study presents an improved nonhomogeneous grey model by incorporating the dynamic integral mean value theorem and fractional accumulation simultaneously. …”
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Existence and Uniqueness of Solution for Perturbed Nonautonomous Systems with Nonuniform Exponential Dichotomy by Yong-Hui Xia, Xiaoqing Yuan, Kit Ian Kou, Patricia J. Y. Wong

“…The technique employed to prove Theorem 4 is the highlight of this paper.…”
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Nonlinear Adaptive Equivalent Control Based on Interconnection Subsystems for Air-Breathing Hypersonic Vehicles by Chaofang Hu, Yanwen Liu

“…The reformulation of the altitude-flight-path angle dynamics and the attack angle-pitch rate dynamics is constructed into interconnection subsystems with input-to-state stability via small-gain theorem. For the velocity loop, the dynamic inversion controller is designed. …”
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Dynamics and density function of a HTLV-1 model with latent infection and Ornstein-Uhlenbeck process by Yan Ren, Yan Cheng, Yuzhen Chai, Ping Guo

“…Finally, we select suitable data for numerical simulation intending to corroborate the theorem previously established.…”
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