Anti-Periodic Dynamics of Quaternion-Valued Fuzzy Cellular Neural Networks with Time-Varying Delays on Time Scales by Shiping Shen, Bing Li, Yongkun Li

“…Based on inequality analysis techniques on time scales, a fixed point theorem and the theory of calculus on time scales, the existence, and global exponential stability of anti-periodic solutions for this class of neural networks are established. …”
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Global Asymptotic Almost Periodic Synchronization of Clifford-Valued CNNs with Discrete Delays by Yongkun Li, Jianglian Xiang

“…Second, based on the Banach fixed point theorem, we establish the existence and uniqueness of almost periodic solutions of the considered neural networks. …”
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Multiple Solutions for a Class of N-Laplacian Equations with Critical Growth and Indefinite Weight by Guoqing Zhang, Ziyan Yao

“…Using the suitable Trudinger-Moser inequality and the Mountain Pass Theorem, we prove the existence of multiple solutions for a class of N-Laplacian equations with critical growth and indefinite weight -div∇uN-2∇u+VxuN-2u=λuN-2u/xβ+fx,u/xβ+ɛhx, x∈ℝN, u≠0, x∈ℝN, where 0<β<N, V(x) is an indefinite weight, f:ℝN×ℝ→ℝ behaves like exp⁡αuN/N-1 and does not satisfy the Ambrosetti-Rabinowitz condition, and h∈(W1,N(ℝN))*.…”
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On a Nonlocal Multipoint and Integral Boundary Value Problem of Nonlinear Fractional Integrodifferential Equations by Lahcen Ibnelazyz, Karim Guida, Said Melliani, Khalid Hilal

“…First of all, we give some preliminaries and notations that are necessary for the understanding of the manuscript; second of all, we show the existence and uniqueness of the solution by means of the fixed point theory, namely, Banach’s contraction principle and Krasnoselskii’s fixed point theorem. Last, but not least, we give two examples to illustrate the results.…”
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Nonlinear distortion compensation algorithm aided by channel estimation of memoryless power amplifier for OTFS receiver by Zhanjun JIANG, Huan LIU, Huawei ZHANG, Cuiran LI

“…A compensation algorithm for OTFS receiver was proposed to solve the problem of transmission signal distortion caused by the nonlinear characteristics of power amplifier (PA) in the orthogonal time frequency space (OTFS) system.The channel state information was estimated by Bussgang theorem combined with the complex coefficient polynomial of PA and the average energy of the distortion term.Based on it, the transmitted signal was reconstructed with distortion term and the estimated value was updated for the polynomial normalization.Furthermore, the iterative zero-forcing equalization algorithm was employed to complete adaptive compensation analysis of the nonlinear distortion at the receiver.The results show that the nonlinear influence on transmission signals is reduced, which caused by Saleh and Rapp models, and BER performance of OTFS system is improved effectively.…”
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Series Solution of the Multispecies Lotka-Volterra Equations by Means of the Homotopy Analysis Method by A. Sami Bataineh, M. S. M. Noorani, I. Hashim

“…The HAM continuous solution generated by polynomial base functions is of comparable accuracy to the purely numerical fourth-order Runge-Kutta method. The convergence theorem for the three-dimensional case is also given.…”
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Homoclinic Orbits for a Class of Nonperiodic Hamiltonian Systems by Wenping Qin, Jian Zhang, Fukun Zhao

“…Moreover, by applying a generalized linking theorem for strongly indefinite functionals, we establish the existence of homoclinic orbits for asymptotically quadratic nonlinearity as well as the existence of infinitely many homoclinic orbits for superquadratic nonlinearity.…”
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Existence of Positive Solution for BVP of Nonlinear Fractional Differential Equation by Jun-Rui Yue, Jian-Ping Sun, Shuqin Zhang

“…By using the well-known Guo-Krasnoselskii fixed point theorem, we obtain the existence of at least one positive solution for the above problem.…”
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Skein modules of links in cylinders over surfaces by Jens Lieberum

“…For cylinders over the Möbius strip or the projective plane, we derive special properties of the Conway skein module, among them a refinement of a theorem of Hartley and Kawauchi about the Conway polynomial of strongly positive amphicheiral knots in S3. …”
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Dynamics Analysis of the Escapement Mechanism based on the Quantization of Hairspring Stiffness by Shijia Chen, Xiang Gong, Baoyu Huang

“…At the same time, the influence of the pendulum oscillation amplitude on the instantaneous daily rate is predicted and compared with the experimental data, it has good precision to some extent, the simulation results are in line with Airy Theorem. This model could be used to provide useful support in order to optimize the structure of the domestic mechanical watch movement in the future.…”
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Growth and Approximation of Laplace-Stieltjes Transform with p,q-Proximate Order Converges on the Whole Plane by Yong Qin Cui, Hong Yan Xu

“…One purpose of this paper is to study the growth of entire functions defined by Laplace-Stieltjes transform converges on the whole complex plane, by introducing the concept of p,q-proximate order, and one equivalence theorem of the p,q-proximate order of Laplace-Stieltjes transforms is obtained. …”
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Performance analysis of antenna correlation on land mobile satellite based MIMO systems by Yuan LIN, Yuan-zhi HE, Jing-chao WANG, Han HAN

“…The joint effect of spatial correlation and shadowing of channels on the performance of land mobile satellite MIMO system was analyzed.With the help of contour integral,residue theorem and integral of special functions,closed-form approximations of the outage probability (OP) and the average symbol error rate (SER)were derived.The Monte Carlo simulations results were illustrated through several examples in order to assess the impact of correlation coefficient,the number of antenna and different modulation mode on the performance.It shows that although channel correlation and shadowing degrade system gain,significant performance gains can be obtained by multi-satellite MIMO systems compared to relevant single-input single-output (SISO) ones.…”
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Generalized Synchronization of Stochastic Discrete Chaotic System with Poisson Distribution Coefficient by Shao-juan Ma, Duan Dong, Jie Zheng

“…Secondly, a general method for the generalized synchronization of discrete chaotic system with random parameter is presented by Lyapunov stability theory and contraction theorem. Finally, two synchronization examples numerically illustrated that the proposed control scheme is effective for any stochastic discrete system.…”
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Weak Convergence of the Projection Type Ishikawa Iteration Scheme for Two Asymptotically Nonexpansive Nonself-Mappings by Tanakit Thianwan

“…Moreover, weak convergence of projection type Ishikawa iterates of two asymptotically nonexpansive nonself-mappings without any condition on the rate of convergence associated with the two maps in a uniformly convex Banach space is established. Weak convergence theorem without making use of any of the Opial's condition, Kadec-Klee property, or Fréchet differentiable norm is proved. …”
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Periodic Solutions for a Semi-Ratio-Dependent Predator-Prey System with Delays on Time Scales by Xiaoquan Ding, Gaifang Zhao

“…With the help of a continuation theorem based on coincidence degree theory, we establish necessary and sufficient conditions for the existence of periodic solutions. …”
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Analysis of the Dynamical Properties of Discrete Predator-Prey Systems with Fear Effects and Refuges by Wei Li, Chunrui Zhang, Mi Wang

“…The critical coefficients and properties of bifurcating periodic solutions for Flip and Hopf bifurcations are computed using the center manifold theorem and bifurcation theory. Additionally, numerical simulations are employed to illustrate the bifurcation phenomenon and chaos characteristics. …”
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Analytical Solutions for Nonlinear Dispersive Physical Model by Wen-Xiu Ma, Mohamed R. Ali, R. Sadat

“…These symmetries are derivations using the prolongation theorem. Applying the subequation method, we then use the integrating factor property to solve the NLFODE to obtain a few travelling wave solutions to the time FBBM.…”
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Solving Quantum Dynamics with a Lie-Algebra Decoupling Method by Sofia Qvarfort, Igor Pikovski

“…We then prove the Lie-algebra decoupling theorem and apply it to both closed and open dynamics. …”
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Rigidity of Complete Gradient Shrinkers with Pointwise Pinching Riemannian Curvature by Yawei Chu, Dehe Li, Jundong Zhou

“…The arguments mainly rely on algebraic curvature estimates and several analysis tools on Mn,g,f, such as the property of f-parabolic and a Liouville type theorem.…”
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A note on surfaces with prescribed oriented Euclidean Gauss map by Ricardo Sa Earp, Eric Toubiana

“…We present another proof of a theorem due to Hoffman and Osserman in Euclidean space concerning the determination of a conformal immersion by its Gauss map. …”
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