On hypersurfaces in a locally affine Riemannian Banach manifold II by El-Said R. Lashin, Tarek F. Mersal

“…In our previous work (2002), we proved that an essential second-order hypersurface in an infinite-dimensional locally affine Riemannian Banach manifold is a Riemannian manifold of constant nonzero curvature. In this note, we prove the converse, in other words, we prove that a hypersurface of constant nonzero Riemannian curvature in a locally affine (flat) semi-Riemannian Banach space is an essential hypersurface of second order.…”
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Refraction changes in the anterior and posterior corneal surfaces during the early postoperative period following sinus trabeculectomy by V.V. Averich, A.V. Volzhanin, G.B. Egorova

“…An increase in the anterior corneal curvature was usually associated with the vertical meridian and in the posterior corneal curvature — with the horizontal meridian. …”
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The Characteristic Transient Response of a Pressurized Cantilever Pipe Subjected to Transverse Impact at Its Tip by Feng Liu, Yuchao Yang, Yuelei Wu

“…This paper describes an experimental study on the pure bending mechanical behavior of a pressurized pipe and adoption of a measured moment-curvature relationship under different working conditions in numerical simulations for transient pipe-whip prediction. …”
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Multiply Warped Products with a Semisymmetric Metric Connection by Yong Wang

“…We study the Einstein multiply warped products with a semisymmetric metric connection and the multiply warped products with a semisymmetric metric connection with constant scalar curvature, and we apply our results to generalized Robertson-Walker space-times with a semisymmetric metric connection and generalized Kasner space-times with a semisymmetric metric connection and find some new examples of Einstein manifolds with a semisymmetric metric connection and manifolds with constant scalar curvature with a semisymmetric metric connection.…”
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Study on the Meshing Force and Meshing Rigidity of Cylinder Sine Oscillation Tooth Transmission by Zeng Yunyun, Yuan Xinmei, Zhou Sizhu

“…Based on the hypothesis of stretch small distortion and distortion congruity,the model and algorithm of meshing force analysis under theoretical conditions are given.According to the Hertz theory and geometric relation of meshing pair,the meshing rigidity models of the meshing pair are established,and the calculation formulas of the meshing rigidity and the principal curvature of the contact point are deduced.The presented methods is illustrated through an example,and the distributing characteristic of meshing forces,sum of principal curvature and meshing rigidity of this type of transmission device is acquired.The acquired result can be adopted as the analytical base for structure design,vibration analysis.…”
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Shaping Ability of Reciproc, UnicOne, and Protaper Universal in Simulated Root Canals by Etevaldo Matos Maia Filho, Cláudia de Castro Rizzi, Matheus Bandeca Coelho, Sara Freitas Santos, Luzia Mayanne Oliveira Costa, Ceci Nunes Carvalho, Rudys Rodolfo de Jesus Tavarez, Janir Alves Soares

“…Measurements were taken of the quantity of resin removed from the inner and outer walls of the curvature at 6 levels, the curvature angles before and after instrumentation, and the transportation of the apical foramen. …”
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Evaluation of Root Canal Morphology of Mandibular First and Second Premolars Using Cone Beam Computed Tomography in a Defined Group of Dental Patients in Iran by Neda Hajihassani, Neda Roohi, Karim Madadi, Mahin Bakhshi, Maryam Tofangchiha

“…The most prevalent root curvature was a distal curvature in both premolars (71.4% and 74% of first and second premolars, resp.). …”
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Treatment with Autologous Adipose-derived Regenerative Cells for Peyronie’s Disease in Men: The Straight @head Pilot Study by Majken H. Wiborg, Rasmus Krøijer, Birgitte S. Laursen, Wahida Chakari, Charlotte Harken Jensen, Jens Ahm Sørensen, Lars Lund

“…Key findings and limitations: There was no significant difference in curvature after treatment. However, the participants reported subjective improvements, less distress, and a decrease in unhappiness. …”
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Structural Design and Kinematics Simulation of Reconfigurable Modular Fixture Robot based on Automobile Sheet by Zhang Liwang, Ge Weimin, Wang Xiaofeng, Liu Zengchang

“…For the automotive components of the sheet with different curvature radius,a set of reconfigurable modular fixture is designed. …”
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Geometric Description of the Thermodynamics of the Noncommutative Schwarzschild Black Hole by Alexis Larrañaga, Natalia Herrera, Juliana Garcia

“…Using a thermodynamic metric which is invariant with respect to Legendre transformations, we determine the geometry of the space of equilibrium states and show that phase transitions, which correspond to divergencies of the heat capacity, are represented geometrically as singularities of the curvature scalar. This further indicates that the curvature of the thermodynamic metric is a measure of thermodynamic interaction.…”
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Design and Analysis of the Gear Conjugate Profile based on the Sine- curved Benchmark Tooth Profile by Cui Gaoshang, Fan Yuanxun

“…The gear conjugate profile is solved by tooth profile normal method. The meshing line,curvature and relative sliding ratio are analyzed,and then the bending strength is analyzed through the finite element analysis software ANSYS. …”
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Binormal Motion of Curves with Constant Torsion in 3-Spaces by Josu Arroyo, Óscar J. Garay, Álvaro Pámpano

“…We study curve motion by the binormal flow with curvature and torsion depending velocity and sweeping out immersed surfaces. …”
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The Global Symmetry Group of Quantum Spectral Beams and Geometric Phase Factors by Elias Zafiris

“…In the course of this schema, we introduce the notion of Hermitian differential line sheaves or unitary rays and classify their gauge equivalence classes in terms of a global differential invariant given by the de Rham cohomology class of the curvature. Furthermore, we formulate and interpret physically the curvature recognition integrality theorem for unitary rays. …”
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Analytical study on flow of two non-miscible laminar layers of Newtonian fluids in a curved channel with wall slippage by Jafar Hasnain, Nomana Abid

“…It is concluded that the velocities of the immiscible fluids augment by increasing the curvature parameter whereas the temperatures and shear stresses fall. …”
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Energy analysis of PV surfaces in BIPV applications by Molina-Tamayo Santiago, Yesid Moreno Andrés, Mendoza Felipe, Mesa Gabriel Espitia, Osorio- Gómez Gilberto

“…This paper studies the power generation performance of flexible solar panels at different radii of curvature for both concave and convex configurations. …”
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Some Geometric Characterizations of f-Curves Associated with a Plane Curve via Vector Fields by Azeb Alghanemi, Abeer AlGhawazi

“…The differential geometry of plane curves has many applications in physics especially in mechanics. The curvature of a plane curve plays a role in the centripetal acceleration and the centripetal force of a particle traversing a curved path in a plane. …”
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A Family of Integrable Differential-Difference Equations: Tri-Hamiltonian Structure and Lie Algebra of Vector Fields by Ning Zhang, Xi-Xiang Xu

“…Starting from a novel discrete spectral problem, a family of integrable differential-difference equations is derived through discrete zero curvature equation. And then, tri-Hamiltonian structure of the whole family is established by the discrete trace identity. …”
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Increased Corneal Toricity after Long-Term Orthokeratology Lens Wear by Zhi Chen, Jiaqi Zhou, Feng Xue, Xingtao Zhou, Xiaomei Qu

“…Corneal refractive power and manifest refraction were measured and compared before ortho-k and 1 month after discontinuation of ortho-k lens wear. Changes in corneal curvature were analyzed. Corneal curvature data from a historical longitudinal study were used as control. …”
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Numerical Simulations on the Extinguishing Effect of Water Mist System with Different Parameters of Longitudinal Ventilation in Curve Tunnel Fire by Zhizhong Liu, Chen Chen, Mu Liu, Song Wang, Yuzhu Liu

“…Once a fire occurs in a long curve tunnel, the mixing of hot smoke flow and cold air leads to turbulence due to the curvature’s impact. This phenomenon results in a greater thermal pressure difference at the fire source and a substantially greater temperature field than in the straight tunnel. …”
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Dynamic Characteristics of Electrostatically Actuated Shape Optimized Variable Geometry Microbeam by Sha Zhang, Wen-Ming Zhang, Zhi-Ke Peng, Guang Meng

“…We find that the amplitude and resonant frequency of the dynamic response are not monotonically increasing as the curvature of the width function increases and there exists a critical curvature. …”
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