A note on the Boardman theorem by Zhi Lü, Chun-Lian Zhou

“…Let (T,Mn) be a smooth involution on a closed n-dimensional manifold with n≤52dimF. This paper gives three necessary and sufficient conditions that (T,Mn) is a bounding involution.…”
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Properties of the new N $$ \mathcal{N} $$ = 1 AdS4 vacuum of maximal supergravity by Nikolay Bobev, Thomas Fischbacher, Krzysztof Pilch

“…This 14-dimensional scalar manifold contains approximately one quarter of the known critical points. …”
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Characterizing Sparse Spectral Diversity Within a Homogenous Background: Hydrocarbon Production Infrastructure in Arctic Tundra near Prudhoe Bay, Alaska by Daniel Sousa, Latha Baskaran, Kimberley Miner, Elizabeth Josephine Bushnell

“…Dependence on spatial resolution is observed, with substantial degradation of manifold topology as images are blurred from 5 m native ground sampling distance to simulated 30 m ground projected instantaneous field of view of a hypothetical spaceborne sensor. …”
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Stability and Hopf Bifurcation Analysis of a Gene Expression Model with Diffusion and Time Delay by Yahong Peng, Tonghua Zhang

“…We also derive the formulas determining the direction and the stability of Hopf bifurcations by calculating the normal form on the center manifold.…”
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A Note on the Minimal Period Problem for Second Order Hamiltonian Systems by Huafeng Xiao

“…By making use of generalized Nehari manifold, some sufficient conditions are obtained to guarantee the multiplicity and minimality of periodic solutions for second order Hamiltonian systems. …”
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Existence of Multiple Solutions for a -Kirchhoff Problem with Nonlinear Boundary Conditions by Zonghu Xiu, Caisheng Chen

“…By the variational method on the Nehari manifold, we prove that the problem has at least two positive solutions when some conditions are satisfied.…”
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Ground-State Solutions for a Class of N-Laplacian Equation with Critical Growth by Guoqing Zhang, Jing Sun

“…Our proof is based on a suitable Trudinger-Moser inequality, Pohozaev-Pucci-Serrin identity manifold, and mountain pass lemma.…”
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Adventures in physics by Poénaru, Valentin

“…In the 1970s Gérard Toulouse and myself we wrote three papers on how the homotopy groups of the manifold of internal states influenced the defects of ordered media. …”
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Exact Solutions and Localized Structures for Higher-Dimensional Burgers Systems by Yan-ze Peng

“…A (2+1) dimensional Burgers equation and a coupled higher dimensional Burgers system is studied by the singular manifold method. The Bäcklund transformations are obtained. …”
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Minimizing energy among homotopic maps by Pengzi Miao

“…We study an energy minimizing sequence {ui} in a fixed homotopy class of smooth maps from a 3-manifold. After deriving an approximate monotonicity property for {ui} and a continuous version of the Luckhaus lemma (Simon, 1996) on S2, we show that, passing to a subsequence, {ui} converges strongly in W1,2 topology wherever there is small energy concentration.…”
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Asymptotic behaviour of the sectional ring by Wu, Xiaojun

“…The theory of the Okounkov body is a usual tool for analyzing the asymptotic behaviour of the sectional ring of a line bundle over a projective manifold. In this note, combined with the algebraic reduction, we study the asymptotic behaviour of the sectional ring of a line bundle over any arbitrary compact, normal, irreducible complex space.…”
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A Covariant Canonical Quantization of General Relativity by Stuart Marongwe

“…We show that the Ricci flow in a compact matter free manifold serves as the Hamiltonian density of the vacuum as well as a time evolution operator for the vacuum energy density. …”
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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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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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