On p-Laplace Equations with Singular Nonlinearities and Critical Sobolev Exponent by Mohammed El Mokhtar ould El Mokhtar

“…By using the Nehari manifold, Mountain Pass theorem, and Maximum principle theorem, we prove the existence of at least four distinct nontrivial solutions.…”
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Solitary Waves of the Schrödinger Lattice System with Nonlinear Hopping by Ming Cheng

“…Via variation approach and the Nehari manifold argument, we obtain two types of solution: periodic ground state and localized ground state. …”
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Globality-Locality Preserving Maximum Variance Extreme Learning Machine by Yonghe Chu, Hongfei Lin, Liang Yang, Yufeng Diao, Dongyu Zhang, Shaowu Zhang, Xiaochao Fan, Chen Shen, Deqin Yan

“…This method can preserve the global and local manifold structures of data to optimize the projection direction of the classifier. …”
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Derivations of a Sullivan Model and the Rationalized G-Sequence by Oteng Maphane

“…Let Gk,nℂ for 2≤k<n denote the Grassmann manifold of k-dimensional vector subspaces of ℂn. In this paper, we compute, in terms of the Sullivan models, the rational evaluation subgroups and, more generally, the G-sequence of the inclusion G2,nℂ↣G2,n+rℂ for r≥1.…”
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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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Color fundus photograph-based diabetic retinopathy grading via label relaxed collaborative learning on deep features and radiomics features by Chao Zhang, Guanglei Sheng, Jie Su, Lian Duan

“…Additionally, graph constraints based on manifold learning methods can mitigate overfitting caused by label relaxation.…”
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An effective framework for strange metallic transport by Benoît Douçot, Ayan Mukhopadhyay, Giuseppe Policastro, Sutapa Samanta, Hareram Swain

“…We show that a low co-dimension sub-manifold exists in the space of refined semi-holographic theories in which strange metallic behavior is manifested and which can be obtained just by tuning the ratio of the two couplings. …”
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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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Collaborative Superpixelwised PCA for Hyperspectral Image Classification by Chao Yao, Junrui Gu, Zehua Guo, Miao Ma, Qingrui Guo, Gong Cheng

“…Next, the mean vectors of samples within each superpixel are utilized to model the manifold structure of the data. Then, a novel objective function is formulated, which aims to simultaneously preserve the obtained manifold structure between superpixels and the structure within each superpixel. …”
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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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Existence of Multiple High-Energy Solutions for a Kind of Superlinear Second-Order Elliptic Equations by Fangfang Huang, Qiongfen Zhang

“…Under some suitable assumptions on the potential function and nonlinearity, by using variational methods and the method of Nehari manifold, we obtain the existence result of infinitely many high energy solutions for this kind of systems, which improves many relative results in the literature.…”
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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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