Particle approximations of Wigner distributions for n arbitrary observables by Ralph Sabbagh, Olga Movilla Miangolarra, Hamid Hezari, Tryphon T. Georgiou

“…As a side result, we point out a connection between the convergence of these particle approximations and the Mehler-Heine theorem. Finally, we interpret the supports of these quasiprobability distributions in terms of repeated thought experiments.…”
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On escape criterion of an orbit with s-convexity and illustrations of the behavior shifts in Mandelbrot and Julia set fractals. by Khairul Habib Alam, Yumnam Rohen, Naeem Saleem, Maggie Aphane, Asima Razzaque

“…Our study presents a novel orbit with s-convexity, for illustration of the behavior shift in the fractals. We provide a theorem to demonstrate the escape criterion for transcendental cosine functions of the type Tα,β(u) = cos(um)+αu + β, for [Formula: see text] and m ≥ 2. …”
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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

“…Lyapunov's functional method, M-matrix properties, some inequality technique, and nonnegative semimartingale convergence theorem are used in our approach. The obtained conclusions improve some published results.…”
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A Subclass of Analytic Functions Related to k-Uniformly Convex and Starlike Functions by Saqib Hussain, Akhter Rasheed, Muhammad Asad Zaighum, Maslina Darus

“…Some coefficient inequalities, a distortion theorem, the radii of close-to-convexity, and starlikeness and convexity for these classes of functions are studied. …”
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Stability Analysis of Impulsive Stochastic Reaction-Diffusion Cellular Neural Network with Distributed Delay via Fixed Point Theory by Ruofeng Rao, Shouming Zhong

“…This is the first time to employ the fixed point theorem to derive the stability criterion of reaction-diffusion impulsive stochastic CNN with distributed time delays. …”
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Existence of Solutions for Fractional q-Integrodifference Equations with Nonlocal Fractional q-Integral Conditions by Suphawat Asawasamrit, Jessada Tariboon, Sotiris K. Ntouyas

“…By applying the Banach contraction principle, Krasnoselskii’s fixed point theorem, and Leray-Schauder nonlinear alternative, the existence and uniqueness of solutions are obtained. …”
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Positive Solutions of Nonlinear Fractional Differential Equations with Integral Boundary Value Conditions by J. Caballero, I. Cabrera, K. Sadarangani

“…Our analysis relies on a fixed point theorem in partially ordered sets. Moreover, we compare our results with others that appear in the literature.…”
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Extremal Solutions for Caputo Conformable Differential Equations with p-Laplacian Operator and Integral Boundary Condition by Zhongqi Peng, Yuan Li, Qi Zhang, Yimin Xue

“…In this paper, using Banach fixed point theorem, we obtain the uniqueness of the solution of nonlinear and linear Cauchy problem with the conformable derivatives in the Caputo setting, respectively. …”
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Permanence and Almost Periodic Solutions for N-Species Nonautonomous Lotka-Volterra Competitive Systems with Delays and Impulsive Perturbations on Time Scales by Xuxu Yu, Qiru Wang, Yuzhen Bai

“…By using comparison theorems of impulsive dynamic equations on time scales, we obtain sufficient conditions to guarantee the permanence of the system. …”
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Conformally symplectic structures and the Lefschetz condition by Lejmi, Mehdi, Wilson, Scott O.

“…This short note provides a symplectic analogue of Vaisman’s theorem in complex geometry. Namely, for any compact symplectic manifold satisfying the hard Lefschetz condition in degree 1, every locally conformally symplectic structure is in fact globally conformally symplectic, whenever there is a mutually compatible almost complex structure.…”
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Robust Synchronization of Incommensurate Fractional-Order Chaotic Systems via Second-Order Sliding Mode Technique by Hua Chen, Wen Chen, Binwu Zhang, Haitao Cao

“…Based on the chattering free SOSM control scheme, it can be rigorously proved that the dynamics of the synchronization error is globally asymptotically stable by using the Lyapunov stability theorem. Finally, numerical examples are provided to illustrate the effectiveness of the proposed controller design approach.…”
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Positive Solutions of a Two-Point Boundary Value Problem for Singular Fractional Differential Equations in Banach Space by Bo Liu, Yansheng Liu

“…Second, using Ascoli-Arzela theorem, a sufficient condition is obtained for the existence of at least two positive solutions to the considered singular BVP from the convergent subsequence of the approximate problem. …”
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Empirical likelihood based heteroscedasticity diagnostics for varying coefficient partially nonlinear models by Cuiping Wang, Xiaoshuang Zhou, Peixin Zhao

“…Under some mild conditions, the nonparametric version of the Wilks theorem is obtained. Furthermore, simulation studies and a real data analysis are implemented to evaluate the performances of our proposed approaches.…”
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Existence of Positive Solutions to Singular 𝑝-Laplacian General Dirichlet Boundary Value Problems with Sign Changing Nonlinearity by Qiying Wei, You-Hui Su, Subei Li, Xing-Xue Yan

“…By using the well-known Schauder fixed point theorem and upper and lower solution method, we present some existence criteria for positive solution of an 𝑚-point singular 𝑝-Laplacian dynamic equation on time scales with the sign changing nonlinearity. …”
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The Exact Absorbing Conditions Method in the Analysis of Open Electrodynamic Structures: Circular and Coaxial Waveguides by Seil S. Sautbekov, Yuriy K. Sirenko, Lyudmyla G. Velychko, Alexey A. Vertiy

“…The exact absorbing conditions (EAC) have been constructed and used for truncating an unbounded domain of computation in open initial boundary value problems, which describe space-time transformations of electromagnetic waves in axially symmetrical waveguides. The equivalence theorem is proved that gives grounds for rigorous theoretical justification of the EAC-method.…”
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Synchronization of Fractional-Order Chaotic Systems with Gaussian Fluctuation by Sliding Mode Control by Yong Xu, Hua Wang

“…A fractional integral (FI) sliding surface is proposed for synchronizing the uncertain fractional-order system, and then the sliding mode control technique is carried out to realize the synchronization of the given systems. One theorem about sliding mode controller is presented to prove that the proposed controller can make the system achieve synchronization. …”
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Hopf Bifurcation and Stability Analysis of a Congestion Control Model with Delay in Wireless Access Network by Wen-bo Zhao, Xiao-ke Sun, Huicheng Wang

“…Furthermore, the direction and stability of the bifurcating periodic solutions are derived by applying the normal form theory and the center manifold theorem. Finally, some examples and numerical simulations are presented to show the feasibility of the theoretical results.…”
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On Epiorthodox Semigroups by Shouxu Du, Xinzhai Xu, K. P. Shum

“…Because the structure of this kind of orthodox semigroups has not yet been described, we therefore give a structure theorem for the epi-orthodox semigroups.…”
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Another closure operator on preneighbourhood spaces by Partha Ghosh

“…Deeper consequences like the Tychonoff product theorem or the Stone Čech compactifications follow from richer properties of the set of closed morphisms. …”
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Approximate Controllability for Impulsive Riemann-Liouville Fractional Differential Inclusions by Zhenhai Liu, Maojun Bin

“…Secondly, by using the fractional power of operators and a fixed point theorem for multivalued maps, we establish sufficient conditions for the approximate controllability for a class of Riemann-Liouville fractional impulsive differential inclusions, which is a generalization and continuation of the recent results on this issue. …”
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