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Mannheim Curves in Nonflat 3-Dimensional Space Forms [PDF]

Advances in Mathematical Physics, 2015
We consider the Mannheim curves in nonflat 3-dimensional space forms (Riemannian or Lorentzian) and we give the concept of Mannheim curves. In addition, we investigate the properties of nonnull Mannheim curves and their partner curves.
Wenjing Zhao, Donghe Pei, Xinyu Cao
doaj   +2 more sources

MANNHEIM CURVES IN 3-DIMENSIONAL SPACE FORMS [PDF]

Bulletin of the Korean Mathematical Society, 2013
In Euclidean 3-space, Mannheim curves are characterised by the equation \[ \kappa=a(\kappa^2+\tau^2) \] for a constant \(a\neq 0\), where \(\kappa\) and \(\tau\) are the curvature and the torsion of the curve. Similarly, Mannheim partner curves are characterised by \[ \kappa'=\frac{\kappa}{a}(1+a^2\tau^2) \] where \(\kappa'\) represents the derivative ...
Choi, Jin Ho, Kang, Tae Ho, Kim, Young Ho   +2 more
openaire   +4 more sources

Mannheim curves and their partner curves in Minkowski 3-space E13

Demonstratio Mathematica, 2022
The modified orthogonal frame is an important tool to study analytic space curves whose curvatures have discrete zero points. In this article, by using the modified orthogonal frame, Mannheim curves and their partner curves are investigated in Minkowski ...
Elsharkawy Ayman, Elshenhab Ahmed M.
doaj   +2 more sources

Prediction of mortality in secondary peritonitis: a prospective study comparing p-POSSUM, Mannheim Peritonitis Index, and Jabalpur Peritonitis Index

Perioperative Medicine, 2023
Background Risk scoring systems are required to allow accurate prognostication, compare outcomes of surgery, and allow patients to make informed decisions about their health.
Akshant Anil Pathak, Vivek Agrawal, Naveen Sharma, Karan Kumar, Chinmay Bagla, Aakash Fouzdar   +5 more
doaj   +2 more sources

Prognostic Value of the Mannheim Peritonitis Index in Predicting Mortality Following Emergency Surgery for Hollow Viscus Perforation

Journal of Emergencies, Trauma and Shock
Introduction: Perforation peritonitis is a life-threatening emergency associated with high morbidity and mortality. Early risk stratification is vital, particularly in resource-limited settings.
Hong Quan Dang, Van Bi Nguyen, Quoc Viet Cao, Hoai Thuong Duong, Thuong Tri Cao, Van Phu La   +5 more
doaj   +2 more sources

Automated AI detection of thoracic aortic dissection on CT imaging [PDF]

European Radiology Experimental
Background Aortic dissection (AD) is a life-threatening condition. We developed an artificial intelligence (AI) algorithm capable of robust, accurate, and automated AD detection and sub-classification.
Tobias Norajitra, Michael A. Baumgartner, Lucas R. Cusumano, Jesus G. Ulloa, Christian S. Rizzo, Florian Haag, Alexander Hertel, Nils A. Rathmann, Steffen J. Diehl, Stefan O. Schoenberg, Klaus H. Maier-Hein, Johann S. Rink   +11 more
doaj   +2 more sources

Null Darboux Curve Pairs in Minkowski 3-Space

Axioms, 2021
Based on the fundamental theories of null curves in Minkowski 3-space, the null Darboux mate curves of a null curve are defined which can be regarded as a kind of extension for Bertrand curves and Mannheim curves in Minkowski 3-space.
Jinhua Qian, Mingyu Sun, Pei Yin, Young-Ho Kim   +3 more
doaj   +1 more source

Geometry of coupled dispersionless equations with Mannheim curves

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2023
In this paper, a special kind of curve pair associated with each other by the linear dependency between the principal normal vector of the first curve (called Mannheim curve) and the binormal vector of the second curve (called Mannheim partner curve) is ...
Eren Kemal
doaj   +1 more source

Ophthalmology simulation for undergraduate and postgraduate clinical education [PDF]

International Journal of Ophthalmology, 2016
This is a review education paper on the current ophthalmology simulators utilized worldwide for undergraduate and postgraduate training. At present, various simulators such as the EYE Exam Simulator (Kyoto Kagaku Co.
Daniel Shu Wei Ting, Shaun Sebastian Khung Peng Sim, Christine Wen Leng Yau, Mohamad Rosman, Ai Tee Aw, Ian Yew San Yeo   +5 more
doaj   +1 more source

On Some Quasi-Curves in Galilean Three-Space

Axioms, 2023
In this paper, the quasi-frame and quasi-formulas are introduced in Galilean three-space. In addition, the quasi-Bertrand and the quasi-Mannheim curves are studied.
Ayman Elsharkawy, Yusra Tashkandy, Walid Emam, Clemente Cesarano, Noha Elsharkawy   +4 more
doaj   +1 more source