The Strict AKNS Hierarchy: Its Structure and Solutions by G. F. Helminck

“…We show the compatibility of these Lax equations and that they are equivalent to a set of zero curvature relations. We present a linearization of the system and conclude by giving a wide construction of solutions of this hierarchy.…”
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Totally real submanifolds of a complex space form by U-Hang Ki, Young Ho Kim

“…In particular, totally real submanifolds of a complex number space with parallel mean curvature vector are classified.…”
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On Bernstein-Type Theorems in Semi-Riemannian Warped Products by Wenjie Wang, Ximin Liu

“…By using a technique according to Yau (1976) and a reasonable restriction on the mean curvature of the hypersurfaces, we obtain some new Bernstein-type theorems which extend some known results proved by Camargo et al. (2011) and Colares and Lima (2012).…”
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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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Corneal Biomechanics Determination in Healthy Myopic Subjects by Kunliang Qiu, Xuehui Lu, Riping Zhang, Geng Wang, Mingzhi Zhang

“….; all with p≤0.015), but not with corneal curvature or age; CRF was significantly correlated with CCT and IOPg (r=0.52 and 0.70, resp.; all with p<0.001), but not with axial length/refraction, corneal curvature, or age. …”
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Discrete Element Study of Particle Size Distribution Shape Governing Critical State Behavior of Granular Material by Mingdong Jiang, Daniel Barreto, Zhi Ding, Kaifang Yang

“…Additionally, a decrease in the coefficient of curvature (C_c) would also move the CSL downward but with negligible rotation. …”
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Damage Identification by Using a Self-Synchronizing Multipoint Laser Doppler Vibrometer by Chong Yang, Yu Fu, Jianmin Yuan, Min Guo, Keyu Yan, Huan Liu, Hong Miao, Changchun Zhu

“…The results show that the artificial crack can be identified precisely from the change of natural frequencies and the difference of mode shape curvature squares.…”
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Cyclic Fatigue Resistance of Nickel–Titanium Rotary Instruments after Simulated Clinical Use by Hana R. Ubaed, Diyar Kh. Bakr

“…Then, all the instruments underwent cyclic fatigue testing in an artificial stainless steel canal with a 50° canal curvature and a radius of curvature of 5 mm. The time and number of cycles to failure (NCF) were recorded. …”
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A graphene-based photo-electro-thermal metamaterial for soft fixtures with superior grasping performance by Bowen Yang, Xuanchen Dong, Wenhao Lv, Wenzhuo Liu, Mengying Lu, Zhe Liu, Tonghui Lu, Xianglin Li, Song Lv

“…The SSM achieved rapid response (<5 s), low actuation energy (≤0.22 W cm⁻2 or ≤3.55 V), and large bending curvature (>0.18 mm⁻1), surpassing conventional designs in response speed (226.2% faster) and curvature (249.1% higher). …”
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Bicubic ribbon surface by V. A. Korotkiy, E. A. Usmanova

“…Theorem 2 contains conditions for the continuity of curvature. Examples of calculation and visualization of C1 and C2- smooth ribbon surfaces, consisting of two or three bicubic portions, are presented.…”
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A Cone Bean Computer Tomography Investigation of the Newly Formed Mandibular Anterior Ridge following the Treatment of an Extended Comminuted Fracture: A 12-Year Follow-Up by Pascal Grün, Florian Pfaffeneder-Mantai, Patrick Bandura, Benedikt Schneider, Anna Sophia Bandura, Dritan Turhani

“…Reconstruction of the lost mandibular anterior ridge is very complex due to the natural curvature of the region. Case Presentation. In this case report, the combination of the modified shell technique with autologous bone plates and the guided bone regeneration (GBR) technique was performed on an 18-year-old patient after a comminuted fracture, to ensure new bone formation in the anterior ridge with a natural curvature. …”
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Evaluation of centering ability of XP endo shaper, Edge Evolve and Hyflex CM in simulated curved canals by Van B. Werdina, Ihsan N. Bahnam

“…Conclusions: The study demonstrated that Edge Evolve file maintained curvature significantly better than Hyflex CM and XP endo shaper files. …”
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Constant Strain Rate Uniaxial Compression of Green Sandstone during SHPB Tests Driven by Pendulum Hammer by S. H. Li, W. C. Zhu, L. L. Niu, F. Dai

“…Based on experiments and simulations, parameter effects, including the cambered hammer curvature radius and hammer diameter, length, and impact velocity, on the incident wave shape were examined. …”
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Quaternionic Curves Which Lie on the Special Planes in 4−Dimensional Euclidean Space E4 by İlim Kişi, Sezgin Büyükkütük, Günay Öztürk

“…In this study, some curvature conditions of quaternionic curves are obtained by writing the position vectors of quaternionic curves as linear combinations of new vector fields, named as Di 1≤i≤4, that are produced from Frenet frame fields of the quaternionic curves. …”
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The nonexistence of rank 4 IP tensors in signature (1,3) by Kelly Jeanne Pearson, Tan Zhang

“…We show that there exists no algebraic curvature tensor R on V so that its associated skew-symmetric operator R(⋅) has rank 4 and constant eigenvalues on the Grassmannian of nondegenerate 2-planes in V.…”
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Inverse Problem for a Curved Quantum Guide by Laure Cardoulis, Michel Cristofol

“…We give uniqueness results for the inverse problem associated to the reconstruction of the curvature by using either observations of spectral data or a boot-strapping method.…”
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Classification results for polyharmonic helices in space forms by Branding, Volker

“…Moreover, we show that polyharmonic helices of arbitrary order with non-zero geodesic curvatures to space forms of negative curvature must be geodesics.…”
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The Integrability of a New Fractional Soliton Hierarchy and Its Application by Xiao-ming Zhu, Jian-bing Zhang

“…Two fractional soliton equations are presented generated from the same spectral problem involved in a fractional potential by the zero-curvature representations. They are a kind of special reductions of the famous AKNS system. …”
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Uniqueness of Complete Hypersurfaces in Weighted Riemannian Warped Products by Ning Zhang

“…In this paper, applying the weak maximum principle, we obtain the uniqueness results for the hypersurfaces under suitable geometric restrictions on the weighted mean curvature immersed in a weighted Riemannian warped product I×ρMfn whose fiber M has f-parabolic universal covering. …”
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Screen conformal half-lightlike submanifolds by K. L. Duggal, B. Sahin

“…We prove some results on symmetric induced Ricci tensor and null sectional curvature of this class.…”
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