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Lellis, Nathália Beatriz Manara, and Paulo José Oliveira Cortez. "Comportamento da Lordose Lombar no Exercício Resistido / Lumbar lordosis behavior in Resisted Exercise." REVISTA CIÊNCIAS EM SAÚDE 6, no. 3 (September 30, 2016): 82–93. http://dx.doi.org/10.21876/rcsfmit.v6i3.585.
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Objetivo: Analisar a curvatura lombar durante a execução de exercícios resistidos. Materiais e Métodos: Foram analisadas 81 pessoas, durante a execução de cinco aparelhos diferentes de exercício resistido. Fez-se um registro fotográfico da coluna lombar durante os exercícios, seguido da análise de quatro variáveis: manutenção da lordose fisiológica, hiperlordose, retificação da curvatura e inversão da curvatura. Resultados: Em todos os aparelhos houve a modificação do comportamento da lordose lombar durante a execução dos exercícios. A manutenção da lordose fisiológica, correspondendo a uma posição não errônea ou aceitável, não foi significativa. No aparelho Cadeira Extensora, a manutenção correta da curvatura lombar durante o exercício resistido esteve presente em apenas 35,8%, sendo o aparelho em que menos se manteve a curvatura fisiológica e em que houve a inversão da curva como a modificação mais presente. O Aparelho Voador foi o que mais demonstrou a preservação da postura com uma porcentagem pequena de alteração (76,5%), seguido pelo aparelho Leg Press (preservação de 65,4%) e pelo Pulley Alto (64,2%). No aparelho Cadeira Flexora, pode-se observar um menor número de variedade dos tipos de curvaturas, estando presente apenas a hiperlordose e a lordose fisiológica, com predomínio de 61,7%, estando ausentes a retificação da curva e a inversão da curva. Conclusão: A prática do exercício resistido sem a manutenção da lordose lombar, seja ela por má orientação ou por carga excessiva, está presente na prática regular dos alunos submetidos a análise do presente estudo.Palavras-chave: Curvaturas da Coluna Vertebral, Dor Lombar, Postura, Exercício, Esforço Físico, Levantamento de PesoABSTRACTObjective: To analyze the lumbar curvature while executing resisted exercises. Material and Methods: A total of 81 subjects were analyzed during execution of five different resistance exercise devices. A photographic register of the lumbar spine during the exercise was performed, followed by data analysis of four variables: maintenance of physiological lordosis, hyperlordosis, rectified curvature and reversal of curvature. Results: It was found modification in lumbar lordosis behavior during the execution of all exercises. The maintenance of the physiological lordosis, which would be a not erroneous and acceptable position, was not significant. On the “Stretcher Chair” device, the correct maintenance of the lumbar curvature during resisted exercise was present in only 35.8%. It was the apparatus in which few remained physiological curvature and the most inversion of the curve was present. The “Flying” machine showed the most preservation of posture with a small percentage of change (76.5%), and was followed by the “Leg” unit (65.4%) and “High Pulley” set (64.2%). The “Flexor Chair” device showed the fewer variety in types of curvatures, the hyperlordosis and physiologic lordosis, with a prevalence of 61.7%. Rectification and reversal of the curvature was not observed in this device. Conclusion: The practice of resisted exercise without the maintenance of lumbar lordosis, whether by misdirection or stress, is the regular practice of students subjected to analysis of this study.Keywords: Spinal Curvatures, Low Back Pain, Posture, Exercise, Physical Exertion, Weight Lifting
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WANG, DAN, YAJUN YIN, JIYE WU, and ZHENG ZHONG. "THE INTERACTION POTENTIAL BETWEEN MICRO/NANO CURVED SURFACE BODY WITH NEGATIVE GAUSS CURVATURE AND AN OUTSIDE PARTICLE." Journal of Mechanics in Medicine and Biology 15, no. 06 (December 2015): 1540055. http://dx.doi.org/10.1142/s0219519415400552.
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Based on the negative exponential pair potential ([Formula: see text]), the interaction potential between curved surface body with negative Gauss curvature and an outside particle is proved to be of curvature-based form, i.e., it can be written as a function of curvatures. Idealized numerical experiments are designed to test the accuracy of the curvature-based potential. Compared with the previous results, it is confirmed that the interaction potential between curved surface body and an outside particle has a unified expression of curvatures regardless of the sign of Gauss curvature. Further, propositions below are confirmed: Highly curved surface body may induce driving forces, curvatures and the gradient of curvatures are the essential factors forming the driving forces.
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Bandyopadhyay, Promode R., and Anwar Ahmed. "Turbulent boundary layers subjected to multiple curvatures and pressure gradients." Journal of Fluid Mechanics 246 (January 1993): 503–27. http://dx.doi.org/10.1017/s0022112093000242.
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The effects of abruptly applied cycles of curvatures and pressure gradients on turbulent boundary layers are examined experimentally. Two two-dimensional curved test surfaces are considered: one has a sequence of concave and convex longitudinal surface curvatures and the other has a sequence of convex and concave curvatures. The choice of the curvature sequences were motivated by a desire to study the asymmetric response of turbulent boundary layers to convex and concave curvatures. The relaxation of a boundary layer from the effects of these two opposite sequences has been compared. The effect of the accompanying sequences of pressure gradient has also been examined but the effect of curvature dominates. The growth of internal layers at the curvature junctions have been studied. Measurements of the Górtler and corner vortex systems have been made. The boundary layer recovering from the sequence of concave to convex curvature has a sustained lower skin friction level than in that recovering from the sequence of convex to concave curvature. The amplification and suppression of turbulence due to the curvature sequences have also been studied.
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Bartkowiak, Tomasz, and Christopher A. Brown. "Multiscale 3D Curvature Analysis of Processed Surface Textures of Aluminum Alloy 6061 T6." Materials 12, no. 2 (January 14, 2019): 257. http://dx.doi.org/10.3390/ma12020257.
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The objectives of this paper are to demonstrate the viability, and to validate, in part, a multiscale method for calculating curvature tensors on measured surface topographies with two different methods of specifying the scale. The curvature tensors are calculated as functions of scale, i.e., size, and position from a regular, orthogonal array of measured heights. Multiscale characterization of curvature is important because, like slope and area, it changes with the scale of observation, or calculation, on irregular surfaces. Curvatures can be indicative of the topographically dependent behavior of a surface and, in turn, curvatures are influenced by the processing and use of the surface. Curvatures of surface topographies have not been well- characterized yet. Curvature has been used for calculations in contact mechanics and for the evaluation of cutting edges. Manufactured surfaces are studied for further validation of the calculation method because they provide certain expectations for curvatures, which depend on scale and the degree of curvature. To study a range of curvatures on manufactured surfaces, square edges are machined and honed, then rounded progressively by mass finishing; additionally, a set of surfaces was made by turning with different feeds. Topographic measurements are made with a scanning laser confocal microscope. The calculations use vectors, normal to the measured surface, which are calculated first, then the eigenvalue problem is solved for the curvature tensor. Plots of principal curvatures as a function of position and scale are presented. Statistical analyses show expected interactions between curvature and these manufacturing processes.
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Nurkan, Semra Kaya, and İbrahim Gürgil. "Surfaces with Constant Negative Curvature." Symmetry 15, no. 5 (April 28, 2023): 997. http://dx.doi.org/10.3390/sym15050997.
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In this paper, we have considered surfaces with constant negative Gaussian curvature in the simply isotropic 3-Space by defined Sauer and Strubeckerr. Firstly, we have studied the isotropic II-flat, isotropic minimal and isotropic II-minimal, the constant second Gaussian curvature, and the constant mean curvature of surfaces with constant negative curvature (SCNC) in the simply isotropic 3-space. Surfaces with symmetry are obtained when the mean curvatures are equal. Further, we have investigated the constant Casorati, the tangential and the amalgamatic curvatures of SCNC.
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He, Chen, Michael Kai-Tsun To, Chi-Kwan Chan, and Man Sang Wong. "Significance of recumbent curvature in prediction of in-orthosis correction for adolescent idiopathic scoliosis." Prosthetics and Orthotics International 43, no. 2 (September 7, 2018): 163–69. http://dx.doi.org/10.1177/0309364618798172.
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Background: Prediction of in-orthosis curvature at pre-orthosis stage is valuable for the treatment planning for adolescent idiopathic scoliosis, while the position of spinal curvature assessment that is effective for this prediction is still unknown. Objectives: To compare the spinal curvatures in different body positions for predicting the spinal curvature rendered by orthosis. Study design: A prospective cohort study. Methods: Twenty-two patients with adolescent idiopathic scoliosis (mean Cobb angle: 28.1°± 7.3°) underwent ultrasound assessment of spinal curvature in five positions (standing, supine, prone, sitting bending, prone bending positions) and that within orthosis. Differences and correlations were analyzed between the spinal curvatures in the five positions and that within orthosis. Results: The mean in-orthosis curvature was 11.2° while the mean curvatures in five studied positions were 18.7° (standing), 10.7° (supine), 10.7° (prone), –3.5° (prone bending), and −6.5° (sitting bending). The correlation coefficients of the in-orthosis curvature and that in five studied positions were r = 0.65 (standing), r = 0.76 (supine), r = 0.87 (prone), r = 0.41 (prone bending), and r = 0.36 (sitting bending). Conclusion: The curvature in recumbent positions (supine and prone) is highly correlated to the initial in-orthosis curvature without significant difference. Thus, the initial effect of spinal orthosis could be predicted by the curvature in the recumbent positions (especially prone position) at the pre-orthosis stage. Clinical relevance Prediction of in-orthosis correction at pre-orthosis stage is valuable for spinal orthosis design. This study suggests assessing the spinal curvature in recumbent position (especially prone position) to predict the initial in-orthosis correction for optimizing the orthosis design.
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Garanzha, Vladimir A., Liudmila N. Kudryavtseva, and Dmitry A. Makarov. "Discrete curvatures for planar curves based on Archimedes’ duality principle." Russian Journal of Numerical Analysis and Mathematical Modelling 37, no. 2 (April 1, 2022): 85–98. http://dx.doi.org/10.1515/rnam-2022-0007.
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Abstract We introduce discrete curvatures for planar curves based on the construction of sequences of pairs of mutually dual polylines. For piecewise-regular curves consisting of a finite number of fragments of regular generalized spirals with definite (positive or negative) curvatures our discrete curvatures approximate the exact averaged curvature from below and from above. In order to derive these estimates one should provide a distance function allowing to compute the closest point on the curve for an arbitrary point on the plane.With refinement of the polylines, the averaged curvature over refined curve segments converges to the pointwise values of the curvature and, thus, we obtain a good and stable local approximation of the curvature. For the important engineering case when the curve is approximated only by the inscribed (primal) polyline and the exact distance function is not available, we provide a comparative analysis for several techniques allowing to build dual polylines and discrete curvatures and evaluate their ability to create lower and upper estimates for the averaged curvature.
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Maheshkumar Kankarej, Manisha. "Different Types of Curvature and Their Vanishing Conditions." Academic Journal of Applied Mathematical Sciences, no. 73 (May 2, 2021): 143–48. http://dx.doi.org/10.32861/ajams.73.143.148.
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In the present paper, I studied different types of Curvature like Riemannian Curvature, Concircular Curvature, Weyl Curvature, and Projective Curvature in Quarter Symmetric non-Metric Connection in P-Sasakian manifold. A comparative study of a manifold with a Riemannian connection is done with a P-Sasakian Manifold. Conditions for vanishing for different types of curvature are also a part of the study. Some necessary properties of the Hessian operator are discussed with respect to all curvatures as well.
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Cannon, Kevin S., Benjamin L. Woods, John M. Crutchley, and Amy S. Gladfelter. "An amphipathic helix enables septins to sense micrometer-scale membrane curvature." Journal of Cell Biology 218, no. 4 (January 18, 2019): 1128–37. http://dx.doi.org/10.1083/jcb.201807211.
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Cell shape is well described by membrane curvature. Septins are filament-forming, GTP-binding proteins that assemble on positive, micrometer-scale curvatures. Here, we examine the molecular basis of curvature sensing by septins. We show that differences in affinity and the number of binding sites drive curvature-specific adsorption of septins. Moreover, we find septin assembly onto curved membranes is cooperative and show that geometry influences higher-order arrangement of septin filaments. Although septins must form polymers to stay associated with membranes, septin filaments do not have to span micrometers in length to sense curvature, as we find that single-septin complexes have curvature-dependent association rates. We trace this ability to an amphipathic helix (AH) located on the C-terminus of Cdc12. The AH domain is necessary and sufficient for curvature sensing both in vitro and in vivo. These data show that curvature sensing by septins operates at much smaller length scales than the micrometer curvatures being detected.
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Cheng, Qing-Ming, Shichang Shu, and Young Jin Suh. "Compact hypersurfaces in a unit sphere." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 135, no. 6 (December 2005): 1129–37. http://dx.doi.org/10.1017/s0308210500004303.
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We study curvature structures of compact hypersurfaces in the unit sphere Sn+1(1) with two distinct principal curvatures. First of all, we prove that the Riemannian product is the only compact hypersurface in Sn+1(1) with two distinct principal curvatures, one of which is simple and satisfies where n(n − 1)r is the scalar curvature of hypersurfaces and c2 = (n − 2)/nr. This generalized the result of Cheng, where the scalar curvature is constant is assumed. Secondly, we prove that the Riemannian product is the only compact hypersurface with non-zero mean curvature in Sn+1(1) with two distinct principal curvatures, one of which is simple and satisfies This gives a partial answer for the problem proposed by Cheng.
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Rovenski, Vladimir. "The weighted mixed curvature of a foliated manifold." Filomat 33, no. 4 (2019): 1097–105. http://dx.doi.org/10.2298/fil1904097r.
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We introduce the weighted mixed curvature of an almost product (e.g. foliated) Riemannian manifold equipped with a vector field. We define several qth Ricci type curvatures, which interpolate between the weighed sectional and Ricci curvatures. New concepts of the ?mixed-curvature-dimension condition? and ?synthetic dimension of a distribution? allow us to renew the estimate of the diameter of a compact Riemannian foliation and splitting results for almost product manifolds of nonnegative/nonpositive weighted mixed scalar curvature. We also study the Toponogov?s type conjecture on dimension of a totally geodesic foliation with positive weighted mixed sectional curvature.
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Larsen, Andreas Haahr. "Molecular Dynamics Simulations of Curved Lipid Membranes." International Journal of Molecular Sciences 23, no. 15 (July 22, 2022): 8098. http://dx.doi.org/10.3390/ijms23158098.
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Eukaryotic cells contain membranes with various curvatures, from the near-plane plasma membrane to the highly curved membranes of organelles, vesicles, and membrane protrusions. These curvatures are generated and sustained by curvature-inducing proteins, peptides, and lipids, and describing these mechanisms is an important scientific challenge. In addition to that, some molecules can sense membrane curvature and thereby be trafficked to specific locations. The description of curvature sensing is another fundamental challenge. Curved lipid membranes and their interplay with membrane-associated proteins can be investigated with molecular dynamics (MD) simulations. Various methods for simulating curved membranes with MD are discussed here, including tools for setting up simulation of vesicles and methods for sustaining membrane curvature. The latter are divided into methods that exploit scaffolding virtual beads, methods that use curvature-inducing molecules, and methods applying virtual forces. The variety of simulation tools allow researcher to closely match the conditions of experimental studies of membrane curvatures.
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Hagstrum, Melissa B., and John A. Hildebrand. "The Two-Curvature Method for Reconstructing Ceramic Morphology." American Antiquity 55, no. 2 (April 1990): 388–403. http://dx.doi.org/10.2307/281657.
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Prehistoric ceramic containers were tools used in culinary and ceremonial activity. The archaeological record preserves fragmentary remains of these ceramic tools, challenging the archaeologist to interpret their use and function from potsherds rather than from whole pots. We introduce the two-curvature method for reconstructing ceramic vessel shape and volume from assemblages of potsherds. Each point on a ceramic vessel or sherd has two dimensions of curvature, profile and axial. Profile curvature is sensitive to vessel shape, and axial curvature is sensitive to vessel diameter. Since vessel curvature and sherd curvature are the same, measuring profile and axial curvatures of potsherds provides information on parent-vessel shape and size. The two-curvature method is tested with replicated vessels, and its accuracy for measuring vessel parameters from sherd curvatures is assessed. Vessel parameters are estimated accurately from average-sherd-curvature measurements. Data gathered by using this method, on an archaeological assemblage of Kumeyaay ceramics from southern California, show that Kumeyaay pottery consists of 85–90 percent open-mouth hemispherical bowls and 10–15 percent closed-mouth spherical ollas. Through time, Kumeyaay vessel volume increased while vessel shape remained consistent.
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Tripathi, Mukut Mani, and Jeong-Sik Kim. "C-totally real submanifolds in (κ,μ)-contact space forms." Bulletin of the Australian Mathematical Society 67, no. 1 (February 2003): 51–65. http://dx.doi.org/10.1017/s0004972700033517.
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We obtain a basic B,-Y. Chen's inequality for a C-totally real submanifold in a (κ,μ)-contact space form involving intrinsic invariants, namely the scalar curvature and the sectional curvatures of the submanifold on left hand side and the main extrinsic invariant, namely the squared mean curvature on the right hand side. Inequalities between the squared mean curvature and Ricci curvature and between the squared mean curvature and κ-Ricci curvature are also obtained. These results are applied to get corresponding results for C-totally real submanifolds in a Sasakian space form.
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Bartkowiak, Tomasz, and Christopher Brown. "Multi-scale curvature tensor analysis of machined surfaces." Archives of Mechanical Technology and Materials 36, no. 1 (December 1, 2016): 44–50. http://dx.doi.org/10.1515/amtm-2016-0009.
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Abstract This paper demonstrates the use of multi-scale curvature analysis, an areal new surface characterization technique for better understanding topographies, for analyzing surfaces created by conventional machining and grinding. Curvature, like slope and area, changes with scale of observation, or calculation, on irregular surfaces, therefore it can be used for multi-scale geometric analysis. Curvatures on a surface should be indicative of topographically dependent behavior of a surface and curvatures are, in turn, influenced by the processing and use of the surface. Curvatures have not been well characterized previously. Curvature has been used for calculations in contact mechanics and for the evaluation of cutting edges. In the current work two parts were machined and then one of them was ground. The surface topographies were measured with a scanning laser confocal microscope. Plots of curvatures as a function of position and scale are presented, and the means and standard deviations of principal curvatures are plotted as a function of scale. Statistical analyses show the relations between curvature and these two manufacturing processes at multiple scales.
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Byrum, Christopher R. "Analysis by High-Speed Profile of Jointed Concrete Pavement Slab Curvatures." Transportation Research Record: Journal of the Transportation Research Board 1730, no. 1 (January 2000): 1–9. http://dx.doi.org/10.3141/1730-01.
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A high-speed pavement profile analysis method that detects curvature present in the wheelpaths of jointed concrete pavement slabs is presented. This technique can be used to analyze slab curvatures present in pavements and caused by curling and warping forces. The FHWA Long-Term Pavement Performance (LTPP) program has obtained high-speed elevation profiles for the jointed concrete pavements in the study. This profile analysis method reads an LTPP profile and detects imperfections in the road curvature profile, which typically are joints and cracks. It then analyzes the slab regions (intact slab segments) between these numerical imperfections for the presence of curvature. The result of a profile analysis is a road profile index—the curvature index—which represents the average slab curvature present along the wheelpaths for the profile. This profile analysis method was applied to more than 1,100 LTPP GPS3 profiles. The range of the slab curvatures encountered is described, and some key factors related to apparent locked-in curvatures (related to warping and construction) are discussed. The amount of locked-in curvature in slabs significantly affects slab behavior and long-term pavement performance. Curvature information should be available to pavement rehabilitation engineers making fix type and funding decisions for pavements. This new analysis method could be implemented rapidly in routine pavement profile analysis and pavement management systems.
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Koc, Władysław, and Katarzyna Palikowska. "Determination of the optimal curvature of the turnout diverging track for HSR using dynamic analysis." Transportation Overview - Przeglad Komunikacyjny 2017, no. 10 (October 1, 2017): 1–11. http://dx.doi.org/10.35117/a_eng_17_10_01.
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The paper presents an analytical method of identifying the curvature of the turnout diverging track consisting of sections of varying curvature. Such turnout is mainly applied on High Speed Railway. Both linear and nonlinear (polynomial) curvatures of the turnout diverging track are considered in the paper. Obtained solutions enable to assume curvature values at the beginning and end point of the geometrical layout of the turnout.The paper focus on a fundamental and unexplained so far issue connected with selection of the most favourable curvature section from the operational requirements point of view. In order to determine the optimal curvature a dynamic analysis has been carried out on the several representative cases. It has been indicated that, used in railway practice, clothoid sections with nonzero curvatures at the beginning and end points of the turnout should be verified. It has been proved that the turnout with nonlinear curvature reaching zero values at the extreme points of the geometrical layout is the most favourable.
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CHENG, XINYUE, and ZHONGMIN SHEN. "RANDERS METRICS OF SCALAR FLAG CURVATURE." Journal of the Australian Mathematical Society 87, no. 3 (December 2009): 359–70. http://dx.doi.org/10.1017/s1446788709000408.
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AbstractWe study an important class of Finsler metrics, namely, Randers metrics. We classify Randers metrics of scalar flag curvature whose S-curvatures are isotropic. This class of Randers metrics contains all projectively flat Randers metrics with isotropic S-curvature and Randers metrics of constant flag curvature.
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Huang, Y., and A. J. Rosakis. "Extension of Stoney’s Formula to Arbitrary Temperature Distributions in Thin Film/Substrate Systems." Journal of Applied Mechanics 74, no. 6 (February 9, 2006): 1225–33. http://dx.doi.org/10.1115/1.2744035.
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Current methodologies used for the inference of thin film stress through curvature measurements are strictly restricted to stress and curvature states that are assumed to remain uniform over the entire film/substrate system. By considering a circular thin film/substrate system subject to nonuniform and nonaxisymmetric temperature distributions, we derive relations between the film stresses and temperature, and between the plate system’s curvatures and the temperature. These relations featured a “local” part that involves a direct dependence of the stress or curvature components on the temperature at the same point, and a “nonlocal” part that reflects the effect of temperature of other points on the location of scrutiny. Most notably, we also derive relations between the polar components of the film stress and those of system curvatures which allow for the experimental inference of such stresses from full-field curvature measurements in the presence of arbitrary nonuniformities. These relations also feature a “nonlocal” dependence on curvatures making full-field measurements of curvature a necessity for the correct inference of stress. Finally, it is shown that the interfacial shear tractions between the film and the substrate are related to the gradients of the first curvature invariant and can also be inferred experimentally.
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Wikstro¨m, A., and P. Gudmundson. "Thermal Deformation of Initially Curved Substrates Coated by Thin Inhomogeneous Layers." Journal of Applied Mechanics 68, no. 2 (October 19, 2000): 298–303. http://dx.doi.org/10.1115/1.1357169.
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Thermal curvature changes and membrane strains are analyzed for elastic shallow shell substrates which are coated by thin, generally inelastic, inhomogeneous and anisotropic layers. The analysis is restricted to linear kinematics. It is shown that the deformation is governed by the corresponding solution for a flat substrate and a correction due to the initial curvature. The correction is determined from a shallow shell problem for the bare substrate with a loading expressed by the coefficients of thermal curvature for the substrate/layer system. For constant initial curvatures, certain analytic solutions are presented. For situations when the initial deflection of the substrate is much larger than the substrate thickness, a boundary layer solution is derived. In the particular case of a circular isotropic substrate with a spherical initial curvature and a coating of arbitrary anisotropy, the solution is presented in closed form. For nonflat substrates, measured curvatures can generally not be used to extract layer stresses without a proper compensation for the initial curvature. In the paper, it is explicitly presented how to accurately compensate for a spherical initial curvature. The results are particularly discussed in relation to curvature measurements on Silicon substrates.
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Shichang, Shu. "Complete spacelike hypersurfaces in a de Sitter space." Bulletin of the Australian Mathematical Society 73, no. 1 (February 2006): 9–16. http://dx.doi.org/10.1017/s0004972700038570.
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In this paper, we characterise the n-dimensional (n ≥ 3) complete spacelike hypersurfaces Mn in a de Sitter space with constant scalar curvature and with two distinct principal curvatures. We show that if the multiplicities of such principal curvatures are greater than 1, then Mn is isometric to Hk (sinh r) × Sn−k (cosh r), 1 < k < n − 1. In particular, when Mn is the complete spacelike hypersurfaces in with the scalar curvature and the mean curvature being linearly related, we also obtain a characteristic Theorem of such hypersurfaces.
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MOGHADDAM, HAMID REZA SALIMI. "ON THE RANDERS METRICS ON TWO-STEP HOMOGENEOUS NILMANIFOLDS OF DIMENSION FIVE." International Journal of Geometric Methods in Modern Physics 08, no. 03 (May 2011): 501–10. http://dx.doi.org/10.1142/s0219887811005257.
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In this paper we study the geometry of simply connected two-step nilpotent Lie groups of dimension five. We give the Levi–Civita connection, curvature tensor, sectional and scalar curvatures of these spaces and show that they have constant negative scalar curvature. Also we show that the only space which admits left-invariant Randers metric of Berwald type has three-dimensional center. In this case the explicit formula for computing flag curvature is obtained and it is shown that flag curvature and sectional curvature have the same sign.
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WU, B. Y. "ON COMPLETE SPACELIKE HYPERSURFACES WITH CONSTANT m-TH MEAN CURVATURE IN AN ANTI-DE SITTER SPACE." International Journal of Mathematics 21, no. 05 (May 2010): 551–69. http://dx.doi.org/10.1142/s0129167x10006239.
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We investigate complete spacelike hypersurfaces in an Anti-de Sitter space with constant m-th mean curvature and two distinct principal curvatures. By using Otsuki's idea, we obtain some global classification results. For their application, we obtain some characterizations for hyperbolic cylinders. We prove that the only complete spacelike hypersurfaces in Anti-de Sitter (n + 1)-spaces (n ≥ 3) of constant mean curvature or constant scalar curvature with two distinct principal curvatures λ and μ satisfying inf (λ - μ)2 > 0 are the hyperbolic cylinders. It is a little surprising that the corresponding result does not hold for m-th mean curvature when m > 2. We also obtain some global rigidity results for hyperbolic cylinders in terms of square length of the second fundamental form.
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Özgür, Cihan, and Adela Mihai. "Chen Inequalities for Submanifolds of Real Space Forms with a Semi-Symmetric Non-Metric Connection." Canadian Mathematical Bulletin 55, no. 3 (September 1, 2012): 611–22. http://dx.doi.org/10.4153/cmb-2011-108-1.
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AbstractIn this paper we prove Chen inequalities for submanifolds of real space forms endowed with a semi-symmetric non-metric connection, i.e., relations between the mean curvature associated with a semi-symmetric non-metric connection, scalar and sectional curvatures, Ricci curvatures and the sectional curvature of the ambient space. The equality cases are considered.
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Ruffino, Roberta, Maciej Jankowski, Oleg Konovalov, Francesco Punzo, Nunzio Tuccitto, and Giovanni Li-Destri. "Modulating Polymer Ultrathin Film Crystalline Fraction and Orientation with Nanoscale Curvature." Polymers 15, no. 22 (November 18, 2023): 4453. http://dx.doi.org/10.3390/polym15224453.
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We investigated the effect of nanoscale curvature on the structure of thermally equilibrated poly-3-hexylthiophene (P3HT) ultrathin films. The curvature-induced effects were investigated with synchrotron grazing incidence X-ray diffraction (GIXRD) and atomic force microscopy (AFM). Our results demonstrate that nanoscale curvature reduces the polymer crystalline fraction and the crystal length. The first effect is strongest for the lowest curvature and results in a decrease in the out-of-plane thickness of the polymer crystals. On the other hand, the crystal in-plane length decreases with the increase in substrate curvature. Finally, the semi-quantitative analysis of crystal anisotropy shows a marked dependence on the substrate curvature characterized by a minimum at curvatures between 0.00851 nm−1 and 0.0140 nm−1. The results are discussed in terms of a curvature-dependent polymer fraction, which fills the interstices between neighboring particles and cannot crystallize due to extreme space confinement. This fraction, whose thickness is highest at the lowest curvatures, inhibits the crystal nucleation and the out-of-plane crystal growth. Moreover, because of the adhesion to the curved portion of the substrates, crystals adopt a random orientation. By increasing the substrate curvature, the amorphous fraction is reduced, leading to polymer films with higher crystallinity. Finally, when the thickness of the film exceeds the particle diameter, the curvature no longer affects the crystal orientation, which, similarly to the flat case, is predominantly edge on.
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Defever, Filip. "Conformally flat hypersurfaces with constant Gauss-Kronecker curvature." Bulletin of the Australian Mathematical Society 61, no. 2 (April 2000): 207–16. http://dx.doi.org/10.1017/s0004972700022218.
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We consider 3-dimensional conformally flat hypersurfaces of E4 with constant Gauss-Kronecker curvature. We prove that those with three different principal curvatures must necessarily have zero Gauss-Kronecker curvature.
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Deszcz, Ryszard, Miroslava Petrovic-Torgasev, Zerrin Şentürk, and Leopold Verstraelen. "Characterization of the pseudo-symmetries of ideal Wintgen submanifolds of dimension 3." Publications de l'Institut Math?matique (Belgrade) 88, no. 102 (2010): 53–65. http://dx.doi.org/10.2298/pim1002053d.
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Recently, Choi and Lu proved that the Wintgen inequality ? ? H2??? +k, (where ? is the normalized scalar curvature and H2, respectively ??, are the squared mean curvature and the normalized scalar normal curvature) holds on any 3-dimensional submanifold M3 with arbitrary codimension m in any real space form ~M3+m(k) of curvature k. For a given Riemannian manifold M3, this inequality can be interpreted as follows: for all possible isometric immersions of M3 in space forms ~M3+m(k), the value of the intrinsic curvature ? of M puts a lower bound to all possible values of the extrinsic curvature H2 ? ?? + k that M in any case can not avoid to ?undergo" as a submanifold of ?M. From this point of view, M is called a Wintgen ideal submanifold of ~M when this extrinsic curvature H2 ??? +k actually assumes its theoretically smallest possible value, as given by its intrinsic curvature ?, at all points of M. We show that the pseudo-symmetry or, equivalently, the property to be quasi-Einstein of such 3-dimensional Wintgen ideal submanifolds M3 of M~3+m(k) can be characterized in terms of the intrinsic minimal values of the Ricci curvatures and of the Riemannian sectional curvatures of M and of the extrinsic notions of the umbilicity, the minimality and the pseudo-umbilicity of M in ~M.
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Decu, Simona, and Gabriel-Eduard Vîlcu. "Casorati Inequalities for Statistical Submanifolds in Kenmotsu Statistical Manifolds of Constant ϕ-Sectional Curvature with Semi-Symmetric Metric Connection." Entropy 24, no. 6 (June 8, 2022): 800. http://dx.doi.org/10.3390/e24060800.
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In this paper, we prove some inequalities between intrinsic and extrinsic curvature invariants, namely the normalized δ-Casorati curvatures and the scalar curvature of statistical submanifolds in Kenmotsu statistical manifolds of constant ϕ-sectional curvature that are endowed with semi-symmetric metric connection. Furthermore, we investigate the equality cases of these inequalities. We also describe an illustrative example.
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SIDDIQUI, ALIYA NAAZ, and MOHAMMAD HASAN SHAHID. "Optimizations on Statistical Hypersurfaces with Casorati Curvatures." Kragujevac Journal of Mathematics 45, no. 03 (May 2021): 449–63. http://dx.doi.org/10.46793/kgjmat2103.449s.
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In the present paper, we study Casorati curvatures for statistical hypersurfaces. We show that the normalized scalar curvature for any real hypersurface (i.e., statistical hypersurface) of a holomorphic statistical manifold of constant holomorphic sectional curvature k is bounded above by the generalized normalized δ−Casorati curvatures and also consider the equality case of the inequality. Some immediate applications are discussed.
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Wang, Bin, Wenzhe Cai, and Qingxuan Shi. "Simplified Data-Driven Model for the Moment Curvature of T-Shaped RC Shear Walls." Advances in Civil Engineering 2019 (November 3, 2019): 1–16. http://dx.doi.org/10.1155/2019/9897827.
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Sectional deformation quantities, such as curvature and ductility, are of prime significance in the displacement-based seismic design and performance evaluation of structural members. However, few studies on the estimates of curvatures at different limit states have been performed on asymmetric flanged walls. In this paper, a parametric study was performed for a series of T-shaped wall cross-sections based on moment-curvature analyses. By investigating the effects of the axial load ratio, reinforcement content, material properties, and geometric parameters on curvatures at the yield and ultimate limit state, we interpret the variation in curvature with different influencing factors in detail according to the changes of the neutral axis depth. Based on the regression analyses of the numerical results of 4941 T-shaped cross-sections, simple expressions to estimate the yield curvature and ultimate curvature for asymmetric flanged walls are developed, and simplified estimates of the ductility capacity including curvature ductility and displacement ductility are further deduced. By comparing with the experimental results, we verify the accuracy of the proposed formulas. Such simple expressions will be valuable for the determination of the displacement response of asymmetric flanged reinforced concrete walls.
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Ali, Danish, Johann Davidov, and Oleg Mushkarov. "Holomorphic curvatures of twistor spaces." International Journal of Geometric Methods in Modern Physics 11, no. 03 (March 2014): 1450022. http://dx.doi.org/10.1142/s0219887814500224.
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We study the twistor spaces of oriented Riemannian 4-manifolds as a source of almost Hermitian 6-manifolds of constant or strictly positive holomorphic, Hermitian and orthogonal bisectional curvatures. In particular, we obtain explicit formulas for these curvatures in the case when the base manifold is Einstein and self-dual, and observe that the "squashed" metric on ℂℙ3 is a non-Kähler Hermitian–Einstein metric of positive holomorphic bisectional curvature. This shows that a recent result of Kalafat and Koca [M. Kalafat and C. Koca, Einstein–Hermitian 4-manifolds of positive bisectional curvature, preprint (2012), arXiv: 1206.3941v1 [math.DG]] in dimension four cannot be extended to higher dimensions. We prove that the Hermitian bisectional curvature of a non-Kähler Hermitian manifold is never a nonzero constant which gives a partial negative answer to a question of Balas and Gauduchon [A. Balas and P. Gauduchon, Any Hermitian metric of constant non-positive (Hermitian) holomorphic sectional curvature on a compact complex surface is Kähler, Math. Z.190 (1985) 39–43]. Finally, motivated by an integrability result of Vezzoni [L. Vezzoni, On the Hermitian curvature of symplectic manifolds, Adv. Geom.7 (2007) 207–214] for almost Kähler manifolds, we study the problem when the holomorphic and the Hermitian bisectional curvatures of an almost Hermitian manifold coincide. We extend the result of Vezzoni to a more general class of almost Hermitian manifolds and describe the twistor spaces having this curvature property.
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Gupta, Ram Shankar, Deepika, and A. Sharfuddin. "Biharmonic hypersurfaces in 5-dimensional non-flat space forms." Advances in Geometry 19, no. 2 (April 24, 2019): 235–50. http://dx.doi.org/10.1515/advgeom-2017-0019.
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Abstract We prove that every biharmonic hypersurface having constant higher order mean curvature Hr for r > 2 in a space form M5(c) is of constant mean curvature. In particular, every such biharmonic hypersurface in 𝕊5(1) has constant mean curvature. There exist no such compact proper biharmonic isoparametric hypersurfaces M in 𝕊5(1) with four distinct principal curvatures. Moreover, there exist no proper biharmonic hypersurfaces in hyperbolic space ℍ5 or in E5 having constant higher order mean curvature Hr for r > 2.
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Decu, Simona, Stefan Haesen, Leopold Verstraelen, and Gabriel-Eduard Vîlcu. "Curvature Invariants of Statistical Submanifolds in Kenmotsu Statistical Manifolds of Constant ϕ-Sectional Curvature." Entropy 20, no. 7 (July 14, 2018): 529. http://dx.doi.org/10.3390/e20070529.
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In this article, we consider statistical submanifolds of Kenmotsu statistical manifolds of constant ϕ-sectional curvature. For such submanifold, we investigate curvature properties. We establish some inequalities involving the normalized δ-Casorati curvatures (extrinsic invariants) and the scalar curvature (intrinsic invariant). Moreover, we prove that the equality cases of the inequalities hold if and only if the imbedding curvature tensors h and h∗ of the submanifold (associated with the dual connections) satisfy h=−h∗, i.e., the submanifold is totally geodesic with respect to the Levi–Civita connection.
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Balkan, Y. S., and N. Aktan. "Almost Kenmotsu $f$-manifolds." Carpathian Mathematical Publications 7, no. 1 (July 6, 2015): 6–21. http://dx.doi.org/10.15330/cmp.7.1.6-21.
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In this paper, we consider a generalization of almost Kenmotsu f-manifolds. We get basic Riemannian curvature, sectional curvatures and scalar curvature properties such type manifolds. Finally, we give two examples to clarify some our results.
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Ji, Yong, Chao Shen, Nian Ren, Lan Ma, Yong Hui Ma, and Xi Chen. "Curvature of Magnetic Field and Its Role on Plasma in Turbulent Magnetosheath." Astrophysical Journal 941, no. 1 (December 1, 2022): 67. http://dx.doi.org/10.3847/1538-4357/aca01b.
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Abstract This study presents statistical features of magnetic field curvature in the magnetosheath region. Two sets of high-quality field and plasma data measured by the Magnetospheric Multiscale mission are analyzed by the multiple-point analysis method. The results include the following: (a) The probability distribution function (PDF) of the curvature exhibits two different power laws consistent with previous studies; the PDF of small curvatures depends on the plasma condition and the PDF of large curvatures shows better agreement. (b) The data validate the derived relation between the current density and the guiding center current as well as the diamagnetic current. (c) The acceleration due to curvature drifts in the perpendicular direction occurs when κ/κ rms is larger than 1, which is a potential mechanism for anisotropic distribution of plasma pressure at large curvatures.
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Cevallos, Carlos, Peter Kovac, and Sharon J. Lowe. "Application of curvatures to airborne gravity gradient data in oil exploration." GEOPHYSICS 78, no. 4 (July 1, 2013): G81—G88. http://dx.doi.org/10.1190/geo2012-0315.1.
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We apply equipotential surface curvatures to airborne gravity gradient data. The mean and differential curvature of the equipotential surface, the curvature of the gravity field line, the zero contour of the Gaussian curvature, and the shape index improve the understanding and geologic interpretation of gravity gradient data. Their use is illustrated in model data and applied to FALCON airborne gravity gradiometer data from the Canning Basin, Australia.
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Vaccaro, Marzia Sara, Francesco Marotti de Sciarra, and Raffaele Barretta. "On the regularity of curvature fields in stress-driven nonlocal elastic beams." Acta Mechanica 232, no. 7 (April 26, 2021): 2595–603. http://dx.doi.org/10.1007/s00707-021-02967-w.
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AbstractElastostatic problems of Bernoulli–Euler nanobeams, involving internal kinematic constraints and discontinuous and/or concentrated force systems, are investigated by the stress-driven nonlocal elasticity model. The field of elastic curvature is output by the convolution integral with a special averaging kernel and a piecewise smooth source field of elastic curvature, pointwise generated by the bending interaction. The total curvature is got by adding nonelastic curvatures due to thermal and/or electromagnetic effects and similar ones. It is shown that fields of elastic curvature, associated with piecewise smooth source fields and bi-exponential kernel, are continuously differentiable in the whole domain. The nonlocal elastic stress-driven integral law is then equivalent to a constitutive differential problem equipped with boundary and interface constitutive conditions expressing continuity of elastic curvature and its derivative. Effectiveness of the interface conditions is evidenced by the solution of an exemplar assemblage of beams subjected to discontinuous and concentrated loadings and to thermal curvatures, nonlocally associated with discontinuous thermal gradients. Analytical solutions of structural problems and their nonlocal-to-local limits are evaluated and commented upon.
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Ross, Nicholas M., Alexander Goettker, Alexander C. Schütz, Doris I. Braun, and Karl R. Gegenfurtner. "Discrimination of curvature from motion during smooth pursuit eye movements and fixation." Journal of Neurophysiology 118, no. 3 (September 1, 2017): 1762–74. http://dx.doi.org/10.1152/jn.00324.2017.
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Smooth pursuit and motion perception have mainly been investigated with stimuli moving along linear trajectories. Here we studied the quality of pursuit movements to curved motion trajectories in human observers and examined whether the pursuit responses would be sensitive enough to discriminate various degrees of curvature. In a two-interval forced-choice task subjects pursued a Gaussian blob moving along a curved trajectory and then indicated in which interval the curve was flatter. We also measured discrimination thresholds for the same curvatures during fixation. Motion curvature had some specific effects on smooth pursuit properties: trajectories with larger amounts of curvature elicited lower open-loop acceleration, lower pursuit gain, and larger catch-up saccades compared with less curved trajectories. Initially, target motion curvatures were underestimated; however, ∼300 ms after pursuit onset pursuit responses closely matched the actual curved trajectory. We calculated perceptual thresholds for curvature discrimination, which were on the order of 1.5 degrees of visual angle (°) for a 7.9° curvature standard. Oculometric sensitivity to curvature discrimination based on the whole pursuit trajectory was quite similar to perceptual performance. Oculometric thresholds based on smaller time windows were higher. Thus smooth pursuit can quite accurately follow moving targets with curved trajectories, but temporal integration over longer periods is necessary to reach perceptual thresholds for curvature discrimination. NEW & NOTEWORTHY Even though motion trajectories in the real world are frequently curved, most studies of smooth pursuit and motion perception have investigated linear motion. We show that pursuit initially underestimates the curvature of target motion and is able to reproduce the target curvature ∼300 ms after pursuit onset. Temporal integration of target motion over longer periods is necessary for pursuit to reach the level of precision found in perceptual discrimination of curvature.
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Hirakui, Yuma, and Takahiro Yajima. "Geometrical Classification of Self-Similar Motion of Two-Dimensional Three Point Vortex System by Deviation Curvature on Jacobi Field." Advances in Mathematical Physics 2021 (October 21, 2021): 1–14. http://dx.doi.org/10.1155/2021/9979529.
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In this study, we geometrically analyze the relation between a point vortex system and deviation curvatures on the Jacobi field. First, eigenvalues of deviation curvatures are calculated from relative distances of point vortices in a three point vortex system. Afterward, based on the assumption of self-similarity, time evolutions of eigenvalues of deviation curvatures are shown. The self-similar motions of three point vortices are classified into two types, expansion and collapse, when the relative distances vary monotonously. Then, we find that the eigenvalues of self-similarity are proportional to the inverse fourth power of relative distances. The eigenvalues of the deviation curvatures monotonically convergent to zero for expansion, whereas they monotonically diverge for collapse, which indicates that the strengths of interactions between point vortices related to the time evolution of spatial geometric structure in terms of the deviation curvatures. In particular, for collapse, the collision point becomes a geometric singularity because the eigenvalues of the deviation curvature diverge. These results show that the self-similar motions of point vortices are classified by eigenvalues of the deviation curvature. Further, nonself-similar expansion is numerically analyzed. In this case, the eigenvalues of the deviation curvature are nonmonotonous but converge to zero, suggesting that the motion of the nonself-similar three point vortex system is also classified by eigenvalues of the deviation curvature.
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Jenmalm, Per, Antony W. Goodwin, and Roland S. Johansson. "Control of Grasp Stability When Humans Lift Objects With Different Surface Curvatures." Journal of Neurophysiology 79, no. 4 (April 1, 1998): 1643–52. http://dx.doi.org/10.1152/jn.1998.79.4.1643.
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Jenmalm, Per, Antony W. Goodwin, and Roland S. Johansson. Control of grasp stability when humans lift objects with different surface curvatures. J. Neurophysiol. 79: 1643–1652, 1998. In previous investigations of the control of grasp stability, humans manipulated test objects with flat grasp surfaces. The surfaces of most objects that we handle in everyday activities, however, are curved. In the present study, we examined the influence of surface curvature on the fingertip forces used when humans lifted and held objects of various weights. Subjects grasped the test object between the thumb and the index finger. The matching pair of grasped surfaces were spherically curved with one of six different curvatures (concave with radius 20 or 40 mm; flat; convex with radius 20, 10, or 5 mm) and the object had one of five different weights ranging from 168 to 705 g. The grip force used by subjects (force along the axis between the 2 grasped surfaces) increased with increasing weight of the object but was modified inconsistently and incompletely by surface curvature. Similarly, the duration and rate of force generation, when the grip and load forces increased isometrically in the load phase before object lift-off, were not influenced by surface curvature. In contrast, surface curvature did affect the minimum grip forces required to prevent frictional slips (the slip force). The slip force was smaller for larger curvatures (both concave and convex) than for flatter surfaces. Therefore the force safety margin against slips (difference between the employed grip force and the slip force) was higher for the higher curvatures. We conclude that surface curvature has little influence on grip force regulation during this type of manipulation; the moderate changes in slip force resulting from changes in curvature are not fully compensated for by changes in grip force.
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SALIMI MOGHADDAM, HAMID REZA. "ON SOME HYPERCOMPLEX 4-DIMENSIONAL LIE GROUPS OF CONSTANT SCALAR CURVATURE." International Journal of Geometric Methods in Modern Physics 06, no. 04 (June 2009): 619–24. http://dx.doi.org/10.1142/s0219887809003710.
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In this paper we study sectional curvature of invariant hyper-Hermitian metrics on simply connected 4-dimensional real Lie groups admitting invariant hypercomplex structure. We give the Levi–Civita connections and explicit formulas for computing sectional curvatures of these metrics and show that all these spaces have constant scalar curvature. We also show that they are flat or they have only non-negative or non-positive sectional curvature.
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Wei, An Chi, and Hsiu Ming Du. "Concentrated Photovoltaic System with Multi-Curvature Fresnel Concentrator." Key Engineering Materials 656-657 (July 2015): 628–33. http://dx.doi.org/10.4028/www.scientific.net/kem.656-657.628.
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A multi-curvature Fresnel concentrator is proposed in this study for a concentrated photovoltaic system (CPV) to suppress aberrations. Unlike a conventional Fresnel concentrator with a single curvature, the proposed one integrates several Fresnel concentrators with individual curvatures. An embodiment is designed for a PMMA concentrator comprising four curvatures. The simulated efficiency of the embodiment is 86.4%. The tolerance analyses and the fabrication considerations of the CPV are provided and discussed.
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Faraj, Bestoon Mohammed. "Estimation Accuracy of Root Canal Curvatures from Different Dental Diagnostic Imaging Techniques: An In Vitro Experimental Study." BioMed Research International 2021 (January 13, 2021): 1–8. http://dx.doi.org/10.1155/2021/6699635.
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In clinical endodontics, preoperative estimation of root canal curvature is crucial regarding the prevention of iatrogenic errors. Reproduction of the two-dimensional radiographic images causes certain proximal view curvatures not seen. Therefore, the present study is aimed at investigating the degree of root canal curvature identified in different radiographic views. A total of 60 human permanent single-rooted teeth with varying degrees of curvature were selected. The root canal curvature for each tooth was measured on cone-beam computed tomography (CBCT) images (clinical view), standard digital periapical view (0° angle), digital periapical horizontal parallax view (30° angle), and digital periapical proximal view (0° angle), by using the Schneider method. No statistically significant difference was found in the degree of curvatures estimated on CBCT images and standard digital periapical view (0° angle) in the same tooth. The results revealed a significant difference between the proximal view and the other three groups ( p < 0.05 ). There was no significant difference in this respect between the horizontal parallax view (30° angle), clinical view (CBCT images), and standard digital periapical view ( p > 0.05 ). Proximal view curvatures cannot be predicted or estimated only from examining a clinical view radiograph. A horizontal parallax view (30° angle) is highly recommended as specific guidelines on how to estimate root canal curvature in case difficulty assessment protocols.
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Blaga, Adara M., and Antonella Nannicini. "On curvature tensors of Norden and metallic pseudo-Riemannian manifolds." Complex Manifolds 6, no. 1 (January 1, 2019): 150–59. http://dx.doi.org/10.1515/coma-2019-0008.
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AbstractWe study some properties of curvature tensors of Norden and, more generally, metallic pseudo-Riemannian manifolds. We introduce the notion of J-sectional and J-bisectional curvature of a metallic pseudo-Riemannian manifold (M, J, g) and study their properties.We prove that under certain assumptions, if the manifold is locally metallic, then the Riemann curvature tensor vanishes. Using a Norden structure (J, g) on M, we consider a family of metallic pseudo-Riemannian structures {Ja,b}a,b∈ℝ and show that for a ≠ 0, the J-sectional and J-bisectional curvatures of M coincide with the Ja,b-sectional and Ja,b-bisectional curvatures, respectively. We also give examples of Norden and metallic structures on ℝ2n.
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Tanaka, Minoru, and Kei Kondo. "The topology of an open manifold with radial curvature bounded from below by a model surface with finite total curvature and examples of model surfaces." Nagoya Mathematical Journal 209 (March 2013): 23–34. http://dx.doi.org/10.1017/s0027763000010679.
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AbstractWe construct distinctive surfaces of revolution with finite total curvature whose Gauss curvatures are not bounded. Such a surface of revolution is employed as a reference surface of comparison theorems in radial curvature geometry. Moreover, we prove that a complete noncompact Riemannian manifold M is homeomorphic to the interior of a compact manifold with boundary if the manifold M is not less curved than a noncompact model surface of revolution and if the total curvature of the model surface is finite and less than 2π. By the first result mentioned above, the second result covers a much wider class of manifolds than that of complete noncompact Riemannian manifolds whose sectional curvatures are bounded from below by a constant.
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Iyigün, Esen. "Constant curvature ratios in L6." Filomat 30, no. 3 (2016): 785–89. http://dx.doi.org/10.2298/fil1603785i.
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In this paper, we find a relation between Frenet formulas and harmonic curvatures, and also a relation between Frenet formulas and e-curvature functions of a curve of osculating order 6 in 6 dimensional Lorentzian space L6. Moreover, we give a relation between harmonic curvatures and ccr-curves of a curve in L6.
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Inoguchi, Jun-ichi, Rushan Ziatdinov, and Kenjiro T. Miura. "A Note on Superspirals of Confluent Type." Mathematics 8, no. 5 (May 11, 2020): 762. http://dx.doi.org/10.3390/math8050762.
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Superspirals include a very broad family of monotonic curvature curves, whose radius of curvature is defined by a completely monotonic Gauss hypergeometric function. They are generalizations of log-aesthetic curves, and other curves whose radius of curvature is a particular case of a completely monotonic Gauss hypergeometric function. In this work, we study superspirals of confluent type via similarity geometry. Through a detailed investigation of the similarity curvatures of superspirals of confluent type, we find a new class of planar curves with monotone curvature in terms of Tricomi confluent hypergeometric function. Moreover, the proposed ideas will be our guide to expanding superspirals.
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Fleszar, Andrew J., Alyssa Walker, Pamela K. Kreeger, and Jacob Notbohm. "Substrate curvature induces fallopian tube epithelial cell invasion via cell–cell tension in a model of ovarian cortical inclusion cysts." Integrative Biology 11, no. 8 (August 2019): 342–52. http://dx.doi.org/10.1093/intbio/zyz028.
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Abstract Throughout the body, epithelial tissues contain curved features (e.g. cysts, ducts and crypts) that influence cell behaviors. These structures have varied curvature, with flat structures having zero curvature and structures such as crypts having large curvature. In the ovary, cortical inclusion cysts (CICs) of varying curvatures are found, and fallopian tube epithelial (FTE) cells have been found trapped within these cysts. FTE are the precursor for ovarian cancer, and the CIC niche has been proposed to play a role in ovarian cancer progression. We hypothesized that variations in ovarian CIC curvature that occur during cyst resolution impact the ability of trapped FTE cells to invade into the surrounding stroma. Using a lumen model in collagen gels, we determined that increased curvature resulted in more invasions of mouse FTE cells. To isolate curvature as a system parameter, we developed a novel technique to pattern concave curvatures into collagen gels. When FTE cells were seeded to confluency on curved substrates, increases in curvature increased the number of invading FTE cells and the invasion distance. FTE invasion into collagen substrates with higher curvature depended on matrix metalloproteinases (MMPs), but expression of collagen I degrading Mmps was not different on curved and flat regions. A finite-element model predicted that contractility and cell–cell connections were essential for increased invasion on substrates with higher curvature, while cell–substrate interactions had minimal effect. Experiments supported these predictions, with invasion decreased by blebbistatin, ethylene glycol-bis(β-aminoethyl ether)-N,N,N’,N’-tetraacetic acid (EGTA) or N-cadherin-blocking antibody, but with no effect from a focal adhesion kinase inhibitor. Finally, experimental evidence supports that cell invasion on curved substrates occurs in two phases—a cell–cell-dependent initiation phase where individual cells break away from the monolayer and an MMP-dependent phase as cells migrate further into the collagen matrix.
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Wan, Ying Ming, Ming Bi, and Jing Yun Wang. "A 3D-FEA of Temporomandibular Joint with Reduced Curvature of Curve of Spee." Advanced Materials Research 926-930 (May 2014): 2876–79. http://dx.doi.org/10.4028/www.scientific.net/amr.926-930.2876.
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Temporomandibular joint (TMJ) is a weight-bearing joint[1],its biomechanical environment is closely related to bite force. Morphological characteristics of occlusal is an important guide to the bite force conduction. This conduction has an important impact on environmental stress in TMJ. Spee curve is one of the important morphological features of dentition,but study of its curvature changes in relations to joint stress is rarely reported . This study aimed to analyze stress distribution in TMJ when curvature of Curve of Spee decreased. In this study, two kinds of 3D model with diffirent curvatures of Curve of Spee were designed. Model 0: the normal, the curvature was 2.50mm. The vertex was at the cuspis of the second premolar. Model 1: the curvature was 0. Then analyzed by 3D-FEM. The final results validated that the anterior surface of condyle and intermediate zone of articular disc were the weight-bearing areas in TMJ. The stress increased along with curvatures of Curve of Spee decreased.
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Decu, Simona, Stefan Haesen, and Leopold Verstraelen. "Inequalities for the Casorati Curvature of Statistical Manifolds in Holomorphic Statistical Manifolds of Constant Holomorphic Curvature." Mathematics 8, no. 2 (February 14, 2020): 251. http://dx.doi.org/10.3390/math8020251.
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In this paper, we prove some inequalities in terms of the normalized δ -Casorati curvatures (extrinsic invariants) and the scalar curvature (intrinsic invariant) of statistical submanifolds in holomorphic statistical manifolds with constant holomorphic sectional curvature. Moreover, we study the equality cases of such inequalities. An example on these submanifolds is presented.