Legendre Invariance and Geometrothermodynamics Description of the 3D Charged-Dilaton Black Hole by Yiwen Han, XiaoXiong Zeng

“…This result is valid for the black hole, therefore, provides a geometrothermodynamics description of black hole phase transitions in terms of curvature singularities.…”
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Estimates for Eigenvalues of the Elliptic Operator in Divergence Form on Riemannian Manifolds by Shenyang Tan, Tiren Huang, Wenbin Zhang

“…We also get universal inequalities for eigenvalues of elliptic operators in divergence form on compact domains of complete submanifolds admitting special functions which include the Hadamard manifolds with Ricci curvature bounded below and any complete manifolds admitting eigenmaps to a sphere.…”
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A Family of Integrable Different-Difference Equations, Its Hamiltonian Structure, and Darboux-Bäcklund Transformation by Xi-Xiang Xu, Meng Xu

“…An integrable family of the different-difference equations is derived from a discrete matrix spectral problem by the discrete zero curvature representation. Hamiltonian structure of obtained integrable family is established. …”
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A Class of Weingarten Surfaces in Euclidean 3-Space by Yu Fu, Lan Li

“…., 2012) by the equation A(grad H)=-H grad H for the mean curvature function H and the Weingarten operator A. …”
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Biharmonic Maps and Laguerre Minimal Surfaces by Yusuf Abu Muhanna, Rosihan M. Ali

“…Estimates of the Gaussian curvature to the Laguerre minimal surface are obtained, and several illustrative examples are given.…”
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A Soliton Hierarchy Associated with a Spectral Problem of 2nd Degree in a Spectral Parameter and Its Bi-Hamiltonian Structure by Yuqin Yao, Shoufeng Shen, Wen-Xiu Ma

“…Associated with so~(3,R), a new matrix spectral problem of 2nd degree in a spectral parameter is proposed and its corresponding soliton hierarchy is generated within the zero curvature formulation. Bi-Hamiltonian structures of the presented soliton hierarchy are furnished by using the trace identity, and thus, all presented equations possess infinitely commuting many symmetries and conservation laws, which implies their Liouville integrability.…”
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CIVA Confirmation of the effect of Wedge Gap on Amplitude by Edward Ginzel, Robert Ginzel

“…Simulations of gap are made for wear-pin adjustment and for small gaps that can occur when a wedge contoured for curvature on a cylinder of one diameter is used on a cylinder that is slightly larger in diameter. …”
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A boundary value problem in the hyperbolic space by P. Amster, G. Keilhauer, M. C. Mariani

“…We consider a nonlinear problem for the mean curvature equation in the hyperbolic space with a Dirichlet boundary data g. …”
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Willmore-Like Tori in Killing Submersions by Manuel Barros, Óscar J. Garay, Álvaro Pámpano

“…A connection with generalized elastica in the base surface of the Killing submersion is found, which is exploited to analyze Willmore tori in Killing submersions and to construct foliations of Killing submersions made up of Willmore tori with constant mean curvature.…”
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Anomaly induced inflation in the minimal quartic extension of Einstein’s gravity by Kerim Demirel, Bayram Tekin

“…Abstract A particular extension of Einstein’s General Relativity up to and including quartic terms in the curvature tensor is minimal in the sense that it has a unique maximally symmetric vacuum and only a massless spin-2 excitation in its spectrum around the vacuum. …”
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Weyl-Euler-Lagrange Equations of Motion on Flat Manifold by Zeki Kasap

“…It is well known that a Riemannian manifold is said to be flat if its curvature is everywhere zero. Furthermore, a flat manifold is one Euclidean space in terms of distances. …”
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Phase Transitions of the BTZ Black Hole in New Massive Gravity by Yun Soo Myung

“…For m2l2>1/2 with m2 being the mass parameter of fourth-order terms and l2 AdS3 curvature radius, the Hawking-Page phase transition occurs between the BTZ black hole and AdS (thermal) soliton. …”
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The Morse Index of Sacks–Uhlenbeck α-Harmonic Maps for Riemannian Manifolds by Amir Shahnavaz, Nader Kouhestani, Seyed Mehdi Kazemi Torbaghan

“…Second, the instability of nonconstant α-harmonic maps is studied with regard to the Ricci curvature criterion of their codomain. Then, we estimate the Morse index for measuring the degree of instability of some particular α-harmonic maps. …”
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Dimethomorph induces heart and vascular developmental defects by disrupting thyroid hormone in zebrafish embryos by You Wei, Yunlong Meng, Kun Jia, Weijian Lu, Yushan Huang, Huiqiang Lu

“…The results showed a concentration-dependent decrease in survival rate and hatching rate, shortened body length, slowed heart rate, and pericardial edema, body curvature and reduced eye size as DMT exposure concentration increased. …”
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Infernal instabilities in negative-triangularity plasmas with negative central shear by X.M. Zhang, L. Li, Y.Q. Liu, Z.Y. Dong, J.W. Li, Y. Liang, F.C. Zhong

“…This is mainly due to less favorable (or even unfavorable) average magnetic curvature near the radial location of the minimum safety factor ( ${q_{{\text{min}}}}$ ) as compared to the pos-D configuration. …”
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Electron Acceleration by Multiple Fast Fermi Reflections at Earth’s Bow Shock by Y. Y. Liu, J. B. Cao, C. M. Liu, Y. T. Song, D. K. Hu

“…Meanwhile, the magnetic field exhibits no variations except an increase in radius of curvature. Based on the results above, we uncover the underlying acceleration scenario. …”
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A Case of Mucosal Cancer of the Stomach Treated by Endoscopic Submucosal Dissection after Which Nodal Metastasis Became Evident by Takashi Obana, Naotaka Fujita, Yutaka Noda, Dai Hirasawa, Kei Ito, Toshiki Sugawara, Yoshihiro Harada, Tetsuya Oohira, Hiroshi Honda, Takashi Sawai

“…Esophagogastroduodenoscopy (EGD) showed a small protruding lesion and a large superficial elevated lesion on the lesser curvature of the stomach (macroscopic type: 0-I and 0-IIa, resp.). …”
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Meridional Considerations of the Centrifugal Compressor Development by C. Xu, R. S. Amano

“…Proper meridional profiles can improve the compressor efficiency and increase the overall pressure ratio at the same blade back curvature.…”
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Controlled Roof Collapse during Secondary Mining in Coal Mines by Ashleigh Hutchinson

“…We consider the range of values of 𝐵 before the displacement and curvature first become singular at 𝐵=𝐵1. The model predicts that for all practical purposes, the beam will break at the clamped end at the pillar. …”
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Geometric Mechanics on Warped Product Semi-Slant Submanifold of Generalized Complex Space Forms by Yanlin Li, Ali H. Alkhaldi, Akram Ali

“…Several results for connected, compact warped product semi-slant submanifolds of nearly Kaehler manifolds are obtained, and they are derived in the context of the Hamiltonian, Dirichlet energy function, gradient Ricci curvature, and nonzero eigenvalue of the Laplacian of the warping functions.…”
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