New Periodic Solutions for the Singular Hamiltonian System by Yi Liao

“…By use of the Cerami-Palais-Smale condition, we generalize the classical Weierstrass minimizing theorem to the singular case by allowing functions which attain infinity at some values. …”
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Normal Form Analysis of Hopf Bifurcation Exemplified by Duffing’s Equation by A.Y.T. Leung, Zhang Qichang, Chen Yushu

“…The results obtained by this method are the same as those obtained by the classical one. The present method is much simpler and can easily be implemented: that is, given the coefficients of the governing equations, the response is obtained directly by substitution.…”
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Quantum Character of Electromagnetic Langmuir Oscillations in Conventional Electron-Ion Plasma by Boris Alexandrovich Veklenko

“…It is shown that the low-temperature plasma near-thermodynamic equilibrium cannot be classical because of a quantum nature of the longitudinal electromagnetic field and electron interaction with Rayleigh-Jeans distribution of Langmuir waves. …”
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An Averaging Principle for Mckean–Vlasov-Type Caputo Fractional Stochastic Differential Equations by Weifeng Wang, Lei Yan, Junhao Hu, Zhongkai Guo

“…In this paper, we want to establish an averaging principle for Mckean–Vlasov-type Caputo fractional stochastic differential equations with Brownian motion. Compared with the classic averaging condition for stochastic differential equation, we propose a new averaging condition and obtain the averaging convergence results for Mckean–Vlasov-type Caputo fractional stochastic differential equations.…”
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Approximation Properties of a New Gamma Operator by Jieyu Huang, Qiulan Qi

“…This paper deals with a kind of modification of the classical Gamma operators defined on the semiaxis which holds fixed functions 1 and e−μx μ>0. …”
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Mathematical analysis and homogenization of the torsion problem by Dag Lukkassen, Annette Meidell, Peter Wall

“…In this paper we address the limitations of the classical formulation of the torsion problem and give a self-contained survey of the function spaces and formulations that are more suitable for analysing the torsional behavior of composite materials. …”
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Stabilities for Nonisentropic Euler-Poisson Equations by Ka Luen Cheung, Sen Wong

“…By analysing the second inertia, we show that the classical solutions of the system with attractive forces blow up in finite time in some special dimensions when the energy is negative. …”
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On a Family of High-Order Iterative Methods under Kantorovich Conditions and Some Applications by S. Amat, C. Bermúdez, S. Busquier, M. J. Legaz, S. Plaza

“…Some numerical experiments, where the analyzed methods present better behavior than some classical schemes, are presented. These applications include the approximation of some quadratic and integral equations.…”
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Coassociative grammar, periodic orbits, and quantum random walk over ℤ by Philippe Leroux

“…Relationships between this coalgebra and the set of periodic orbits of the classical chaotic system x↦2x mod⁡1, x∈[0,1], are also given.…”
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Hardy-Leindler-Type Inequalities via Conformable Delta Fractional Calculus by H. M. Rezk, Wedad Albalawi, H. A. Abd El-Hamid, Ahmed I. Saied, Omar Bazighifan, Mohamed S. Mohamed, M. Zakarya

“…As a result of this, some classical integral inequalities will be obtained. Also, we would have a variety of well-known dynamic inequalities as special cases from our outcomes when α=1.…”
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The Beholder’s Hurt Feeling by Claudia Keller

“…This contribution discusses the implications of Weimar Classicism and its modern consciousness of the hermeneutical difference between antiquity and present on the perception and the methods of restoration. …”
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Neural Network to Solve Concave Games by Zixin Liu, Nengfa Wang

“…On the basis of the Lyapunov stable theory, some stability results are also given. Finally, two classic games’ simulation results are given to illustrate the theoretical results.…”
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A note on the replicator equation with explicit space and global regulation by Alexander S. Bratus, Vladimir P. Posvyanskii, Artem S. Novozhilov

“…For this model, analogues to classical notions of the Nash equilibrium and evolutionary stable state are provided. …”
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Matrix Mappings on the Domains of Invertible Matrices by Muhammed Altun

“…As an application, the necessary and sufficient conditions for the matrix operators between invertible matrix domains of the classical sequence spaces and norms of these operators are given.…”
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Spectral Approach to Derive the Representation Formulae for Solutions of the Wave Equation by Gusein Sh. Guseinov

“…Using spectral properties of the Laplace operator and some structural formula for rapidly decreasing functions of the Laplace operator, we offer a novel method to derive explicit formulae for solutions to the Cauchy problem for classical wave equation in arbitrary dimensions. Among them are the well-known d'Alembert, Poisson, and Kirchhoff representation formulae in low space dimensions.…”
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Horadam Polynomials and a Class of Biunivalent Functions Defined by Ruscheweyh Operator by Waleed Al-Rawashdeh

“…Moreover, we obtain the classical Fekete–Szegö inequality of functions belonging to this class.…”
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Nonsquareness in Musielak-Orlicz-Bochner Function Spaces by Shaoqiang Shang, Yunan Cui, Yongqiang Fu

“…The criteria for nonsquareness in the classical Orlicz function spaces have been given already. …”
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Sturm–Liouville problem with two point nonlocal second type boundary condition by Sigita Pečiulytė, Artūras Štikonas

“… The Sturm–Liouville problemwith one classical boundary condition and other two point second type nonlocal boundary conditions is considered in this paper. …”
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Global Attractor for the Generalized Dissipative KDV Equation with Nonlinearity by Zai-yun Zhang, Zhen-hai Liu

“…We prove existence of a global attractor in space H2(Ω), by using decomposition method with cut-off function and Kuratowskiα-measure in order to overcome the noncompactness of the classical Sobolev embedding.…”
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