scholarly journals Representations of Rectifying Isotropic Curves and Their Centrodes in Complex 3-Space

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1451
Author(s):  
Jinhua Qian ◽  
Pei Yin ◽  
Xueshan Fu ◽  
Hongzeng Wang
Keyword(s):  
Linear Function ◽  
Bessel Functions ◽  
Complex Space ◽  
Three Dimensional ◽  
Arc Length ◽  
Rectifying Curve

In this work, the rectifying isotropic curves are investigated in three-dimensional complex space C3. The conclusion that an isotropic curve is a rectifying curve if and only if its pseudo curvature is a linear function of its pseudo arc-length is achieved. Meanwhile, the rectifying isotropic curves are expressed by the Bessel functions explicitly. Last but not least, the centrodes of rectifying isotropic curves are explored in detail.

scholarly journals Effects of intracorneal ring segments implementation technique and design on corneal biomechanics and keratometry in a personalized computational analysis

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Niksa Mohammadi Bagheri ◽  
Mahmoud Kadkhodaei ◽  
Shiva Pirhadi ◽  
Peiman Mosaddegh
Keyword(s):  
Clinical Data ◽  
Three Dimensional ◽  
Element Model ◽  
Von Mises Stress ◽  
Patient Specific ◽  
Average Error ◽  
Constant Thickness ◽  
Arc Length ◽  
Implementation Techniques ◽  
Von Mises

AbstractThe implementation of intracorneal ring segments (ICRS) is one of the successfully applied refractive operations for the treatment of keratoconus (kc) progression. The different selection of ICRS types along with the surgical implementation techniques can significantly affect surgical outcomes. Thus, this study aimed to investigate the influence of ICRS implementation techniques and design on the postoperative biomechanical state and keratometry results. The clinical data of three patients with different stages and patterns of keratoconus were assessed to develop a three-dimensional (3D) patient-specific finite-element model (FEM) of the keratoconic cornea. For each patient, the exact surgery procedure definitions were interpreted in the step-by-step FEM. Then, seven surgical scenarios, including different ICRS designs (complete and incomplete segment), with two surgical implementation methods (tunnel incision and lamellar pocket cut), were simulated. The pre- and postoperative predicted results of FEM were validated with the corresponding clinical data. For the pre- and postoperative results, the average error of 0.4% and 3.7% for the mean keratometry value ($$\text {K}_{\text{mean}}$$ K mean ) were predicted. Furthermore, the difference in induced flattening effects was negligible for three ICRS types (KeraRing segment with arc-length of 355, 320, and two separate 160) of equal thickness. In contrast, the single and double progressive thickness of KeraRing 160 caused a significantly lower flattening effect compared to the same type with constant thickness. The observations indicated that the greater the segment thickness and arc-length, the lower the induced mean keratometry values. While the application of the tunnel incision method resulted in a lower $$\text {K}_{\text{mean}}$$ K mean value for moderate and advanced KC, the induced maximum Von Mises stress on the postoperative cornea exceeded the induced maximum stress on the cornea more than two to five times compared to the pocket incision and the preoperative state of the cornea. In particular, an asymmetric regional Von Mises stress on the corneal surface was generated with a progressive ICRS thickness. These findings could be an early biomechanical sign for a later corneal instability and ICRS migration. The developed methodology provided a platform to personalize ICRS refractive surgery with regard to the patient’s keratoconus stage in order to facilitate the efficiency and biomechanical stability of the surgery.

scholarly journals Ankle morphometry based on computerized tomography

2017 ◽  
Vol 2 (3) ◽  
pp. 2473011417S0003
Author(s):  
Christian Plaass ◽  
Leif Claassen ◽  
Christina Stukenborg-Colsman ◽  
Daiwei Yao ◽  
Kiriakos Daniilidis ◽  
...  
Keyword(s):  
Ankle Joint ◽  
Three Dimensional ◽  
Ct Scans ◽  
Arc Length ◽  
Success Rates ◽  
Talar Dome ◽  
Talocrural Joint ◽  
Joint Axis ◽  
Ankle Replacement ◽  
Length Width

Category: Ankle Introduction/Purpose: Understanding the morphometry of the ankle joint is crucial to improve total ankle replacement (TAR). Despite improvements of the implant material TAR did not reach comparable success rates to total hip or knee arthroplasty. Recent studies queried whether current designs match with the articular geometry. The present study was performed to evaluate the ankle morphometry and thereby gain information about the joint axis. Methods: We analyzed 96 high-resolution CT-scans of complete caucasian cadaver legs. Using the software Mimics and 3-Matic (Materialize) 22 anatomic parameters of the talocrural joint were assessed, including the length, width and surface area of the tibial and talar bearing areas. Additionally the radii of the bearing areas, the medial distal tibial angle and the height of the talar dome were determined. Therefore we analyzed defined sagittal, axial and frontal planes. Results: The radius of the central trochlea tali was 44.6 ± 4.1 mm (mean ± SD). The central trochlea tali arc length was 40.8 ± 3.0 mm and its width was 27.4 ± 2.5 mm. Additionally we determined 47.0 ± 4.4 mm for the tibial sagittal radius, 27.6 ± 3.0 mm for the tibial arc length and 27.4 ± 2.5 mm for the central tibial width. Conclusion: The present study describes the three-dimensional morphometry of the caucasian ankle joint. Our results might be considered for the development of total ankle replacements.

Remarks on η-parallel real hypersurfaces in ℂP2 and ℂH2

2020 ◽  
Vol 17 (05) ◽  
pp. 2050073
Author(s):  
Yaning Wang
Keyword(s):  
Complex Space ◽  
Space Form ◽  
Three Dimensional ◽  
Shape Operator ◽  
Complex Space Form ◽  
Real Hypersurfaces ◽  
Geodesic Sphere ◽  
Principal Curvatures ◽  
Space Forms ◽  
Complex Dimension

Let [Formula: see text] be a three-dimensional real hypersurface in a nonflat complex space form of complex dimension two. In this paper, we prove that [Formula: see text] is [Formula: see text]-parallel with two distinct principal curvatures at each point if and only if it is locally congruent to a geodesic sphere in [Formula: see text] or a horosphere, a geodesic sphere or a tube over totally geodesic complex hyperbolic plane in [Formula: see text]. Moreover, [Formula: see text]-parallel real hypersurfaces in [Formula: see text] and [Formula: see text] under some other conditions are classified and these results extend Suh’s in [Characterizations of real hypersurfaces in complex space forms in terms of Weingarten map, Nihonkai Math. J. 6 (1995) 63–79] and Kon–Loo’s in [On characterizations of real hypersurfaces in a complex space form with [Formula: see text]-parallel shape operator, Canad. Math. Bull. 55 (2012) 114–126].

scholarly journals On a New type of Tensor on Real Hypersurfaces in Non-Flat Complex Space Forms

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 559
Author(s):  
George Kaimakamis ◽  
Konstantina Panagiotidou
Keyword(s):  
Curvature Tensor ◽  
Complex Space ◽  
Three Dimensional ◽  
Real Hypersurfaces ◽  
Weyl Curvature ◽  
Space Forms ◽  
Hopf Hypersurfaces ◽  
Weyl Curvature Tensor ◽  
New Type ◽  
Complex Space Forms

In this paper the notion of ∗ -Weyl curvature tensor on real hypersurfaces in non-flat complex space forms is introduced. It is related to the ∗ -Ricci tensor of a real hypersurface. The aim of this paper is to provide two classification theorems concerning real hypersurfaces in non-flat complex space forms in terms of ∗ -Weyl curvature tensor. More precisely, Hopf hypersurfaces of dimension greater or equal to three in non-flat complex space forms with vanishing ∗ -Weyl curvature tensor are classified. Next, all three dimensional real hypersurfaces in non-flat complex space forms, whose ∗ -Weyl curvature tensor vanishes identically are classified. The used methods are based on tools from differential geometry and solving systems of differential equations.

scholarly journals The Development of a Repetition-Load Scheme for the Eccentric- Only Bench Press Exercise

2013 ◽  
Vol 38 ◽  
pp. 23-31 ◽  
Author(s):  
Gavin L. Moir ◽  
Kyle F. Erny ◽  
Shala E. Davis ◽  
John J. Guers ◽  
Chad A. Witmer
Keyword(s):  
Linear Function ◽  
Bench Press ◽  
Three Dimensional ◽  
Load Condition ◽  
Vertical Force ◽  
Starting Point ◽  
Stretch Shortening Cycle ◽  
Analysis System ◽  
Repetitions To Failure

Abstract The purpose of the present study was to develop a repetition-load scheme for the eccentric-only bench press exercise. Nine resistance trained men (age: 21.6 ± 1.0 years; 1-repetition maximum [RM] bench press: 137.7 ± 30.4 kg) attended four testing sessions during a four week period. During the first session each subject’s 1-RM bench press load utilizing the stretch-shortening cycle was determined. During the remaining sessions they performed eccentric-only repetitions to failure using supra-maximal loads equivalent to 110%, 120% and 130% of their 1-RM value with a constant cadence (30 reps·min-1). Force plates and a three dimensional motion analysis system were used during these final three sessions in order to evaluate kinematic and kinetic variables. More repetitions were completed during the 110% 1-RM condition compared to the 130% 1-RM condition (p=0.01). Mean total work (p=0.046) as well as vertical force (p=0.049), vertical work (p=0.017), and vertical power output (p=0.05) were significantly greater during the 130% 1-RM condition compared to the 110% 1-RM condition. A linear function was fitted to the number of repetitions completed under each load condition that allowed the determination of the maximum number of repetitions that could be completed under other supra-maximal loads. This linear function predicted an eccentric-only 1-RM in the bench press with a load equivalent to 164.8% 1-RM, producing a load of 227.0 ± 50.0 kg. The repetition-load scheme presented here should provide a starting point for researchers to investigate the kinematic, kinetic and metabolic responses to eccentric-only bench press workouts.

scholarly journals Exact solutions of asymmetric baroclinic quasi-geostrophic dipoles with distributed potential vorticity

2019 ◽  
Vol 868 ◽  
Author(s):  
A. Viúdez
Keyword(s):  
Exact Solution ◽  
Velocity Field ◽  
Potential Vorticity ◽  
Bessel Functions ◽  
Three Dimensional ◽  
Geophysical Flows ◽  
Radial Dependence ◽  
Vortex Dipole ◽  
Second Mode ◽  
Vorticity Anomaly

An exact solution of a baroclinic three-dimensional vortex dipole in geophysical flows with constant background rotation and constant background stratification is provided under the quasi-geostrophic (QG) approximation. The motion of the dipole is unsteady but the potential vorticity contours move rigidly. The vortex comprises three potential vorticity anomaly modes, with a radial dependence given by the spherical Bessel functions and with azimuthal and polar dependences given by the spherical harmonics. The first mode, or spherical mode, accounts for the horizontal asymmetry of the vortex dipole and curvature of the dipole’s horizontal trajectory. The second mode, or dipolar mode, accounts for the speed of displacement of the vortex dipole. A third mode, or vertical tilting mode, accounts for the dipole’s vertical asymmetry. The QG vertical velocity field has two contributions: the first one is octupolar and depends entirely on the dipolar mode, and the second one is dipolar and depends on the nonlinear interaction between dipolar and vertical tilting modes.

Sign in / Sign up

Export Citation Format

Share Document