Standing Wave Solutions for the Discrete Coupled Nonlinear Schrödinger Equations with Unbounded Potentials by Meihua Huang, Zhan Zhou

“…We demonstrate the existence of standing wave solutions of the discrete coupled nonlinear Schrödinger equations with unbounded potentials by using the Nehari manifold approach and the compact embedding theorem. …”
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Blowout bifurcation of chaotic saddles by Tomasz Kapitaniak, Ying-Cheng Lai, Celso Grebogi

“…We describe the blowout bifurcation of chaotic saddles located in the symmetric invariant manifold of coupled systems and discuss dynamical phenomena associated with this bifurcation.…”
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On the Existence of Ground State Solutions of the Periodic Discrete Coupled Nonlinear Schrödinger Lattice by Meihua Huang, Zhan Zhou

“…We study the existence of ground state solutions of the periodic discrete coupled nonlinear Schrödinger lattice by using the Nehari manifold approach combined with periodic approximations. …”
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Bifurcation Analysis for a Predator-Prey Model with Time Delay and Delay-Dependent Parameters by Changjin Xu

“…Using normal form theory and center manifold theory, some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained. …”
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Direction finding method for wideband signals base on consistent focusing by CHEN Hong-guang, YU Sheng-fa, SHEN Zhen-kang

“…MTLS focusing method needs estimating direction of arrival firstly.Estimation bias in only few frequency bins could impair the entire USCM（universal spatial covariance matrix）estimation.Consistent MTLS focusing method was proposed based on the idea of AMI（array manifold interpolating）.Simulations show CMTLS focusing method not only improves the focusing performance,but also reduces the computational burden.…”
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Stability and Hopf Bifurcation Analysis of Coupled Optoelectronic Feedback Loops by Gang Zhu, Junjie Wei

“…Employing the center manifold theorem and normal form method introduced by Hassard et al. (1981), we give an algorithm for determining the Hopf bifurcation properties.…”
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A Schwarz lemma of harmonic maps into metric spaces by Jie Wang

“…We established a Schwarz lemma for harmonic maps from Riemannian manifolds to metric spaces of curvature bounded above in the sense of Alexandrov. …”
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Commerce et logiques d’acteurs dans la région de Kolda au Sénégal by Néné Dia

“…The mini-dairies’s managers and the manifold centers of the dairy basin are developing strategies of collection and marketing which vary from a space to another according to financial means and logistic. hese strategies also reveal the difficulties of the actors.…”
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A simple construction of the Rumin algebra by Case, Jeffrey S.

“…The Rumin algebra of a contact manifold is a contact invariant $C_\infty $-algebra of differential forms which computes the de Rham cohomology algebra. …”
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Stability and Hopf Bifurcation Analysis of a Vector-Borne Disease with Time Delay by Yuanyuan Chen, Ya-Qing Bi

“…The stability and direction of Hopf bifurcation are determined by applying the normal form theory and the center manifold argument.…”
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Rolling Bearing Fault Diagnosis Based on Domain Adaptation and Preferred Feature Selection under Variable Working Conditions by Xiao Yu, Wei Chen, Chuanlong Wu, Enjie Ding, Yuanyuan Tian, Haiwei Zuo, Fei Dong

“…In this framework, an improved domain adaptation method, transfer component analysis with preserving local manifold structure (TCAPLMS), is proposed to reduce the differences in the data distributions between different domain datasets and, at the same time, take the label information of feature dataset and the local manifold structure of feature data into consideration. …”
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An Automatic Recognition Method of Microseismic Signals Based on S Transformation and Improved Gaussian Mixture Model by Kaikai Wang, Chun’an Tang, Ke Ma, Xintang Wang, Qiang Li

“…S transform (ST) and Manifold Learning (ML) methods are introduced to extract the characteristics of the microseismic signals, and Gaussian Mixture Model based on the improved Bee Colony optimization algorithm (IBC-GMM) is established to identify the microseismic signals accurately. …”
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Stability and Hopf Bifurcation of an n-Neuron Cohen-Grossberg Neural Network with Time Delays by Qiming Liu, Sumin Yang

“…Moreover, the direction and stability of Hopf bifurcation are obtained by applying the normal form theory and the center manifold theorem. Numerical simulations are given to illustrate the obtained results.…”
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Hopf Bifurcation Analysis for the Model of the Chemostat with One Species of Organism by Haiyun Bai, Yanhui Zhai

“…By using the normal form theory and center manifold method, we derive the explicit formulas determining the stability and direction of bifurcating periodic solutions. …”
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Bifurcation of a Delayed SEIS Epidemic Model with a Changing Delitescence and Nonlinear Incidence Rate by Juan Liu

“…Directly afterwards, properties of the Hopf bifurcation are determined based on the normal form theory and the center manifold theorem. At last, numerical simulations are carried out to illustrate the obtained theoretical results.…”
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Lightlike Hypersurfaces of Indefinite Generalized Sasakian Space Forms by Dae Ho Jin

“…First we study the general theory for lightlike hypersurfaces of indefinite trans-Sasakian manifold of type (α,β). Next we prove several characterization theorems for lightlike hypersurfaces of an indefinite generalized Sasakian space form.…”
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Local Hopf Bifurcation in a Competitive Model of Market Structure with Consumptive Delays by Xuhui Li

“…The explicit formulas determining the stability and other properties of bifurcating periodic solutions are derived by using normal form theory and center manifold argument. Finally, numerical simulations are given to support the analytical results.…”
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Frobenius integrability of certain $p$-forms on singular spaces by Cao, Junyan, Höring, Andreas

“…Demailly proved that on a smooth compact Kähler manifold the distribution defined by a holomorphic $p$-form with values in an anti-pseudoeffective line bundle is always integrable. …”
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The action of pseudo-differential operators on functions harmonic outside a smooth hyper-surface by Boutet de Monvel, Louis, Colin de Verdière, Yves

“…The goal of this note is to describe the action of pseudo-differential operators on the space of square integrable functions which are harmonic outside a smooth closed hyper-surface of a compact Riemannian manifold.…”
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Some Inequalities for the Omori-Yau Maximum Principle by Kyusik Hong

“…Borbély’s condition for the conclusion of the Omori-Yau maximum principle for the Laplace operator on a complete Riemannian manifold to a second-order linear semielliptic operator L with bounded coefficients and no zeroth order term. …”
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