scholarly journals Timelike Tangent Developable Surfaces and Bonnet Surfaces

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Soley Ersoy ◽  
Kemal Eren
Keyword(s):  
Developable Surface ◽  
3 Dimensional ◽  
Dimensional Minkowski Space ◽  
Base Curve ◽  
Tangent Developable ◽  
Bonnet Surface ◽  
Helicoidal Surface ◽  
The Mean ◽  
Curvature And Torsion ◽  
Necessary And Sufficient

A criterion was given for a timelike surface to be a Bonnet surface in 3-dimensional Minkowski space by Chen and Li, 1999. In this study, we obtain a necessary and sufficient condition for a timelike tangent developable surface to be a timelike Bonnet surface by the aid of this criterion. This is examined under the condition of the curvature and torsion of the base curve of the timelike developable surface being nonconstant. Moreover, we investigate the nontrivial isometry preserving the mean curvature for a timelike flat helicoidal surface by considering the curvature and torsion of the base curve of the timelike developable surface as being constant.

scholarly journals Inextensible Flows of Curves on Lightlike Surfaces

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 224 ◽  
Author(s):  
Zühal Küçükarslan Yüzbaşı ◽  
Dae Yoon
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Sufficient Condition ◽  
Developable Surface ◽  
Necessary And Sufficient Condition ◽  
Partial Differential ◽  
Tangent Developable ◽  
Inextensible Flows ◽  
Necessary And Sufficient ◽  
Three Space

In this paper, we study inextensible flows of a curve on a lightlike surface in Minkowski three-space and give a necessary and sufficient condition for inextensible flows of the curve as a partial differential equation involving the curvatures of the curve on a lightlike surface. Finally, we classify lightlike ruled surfaces in Minkowski three-space and characterize an inextensible evolution of a lightlike curve on a lightlike tangent developable surface.

scholarly journals Null parallel p-equidistant b-scrolls

2014 ◽  
Vol 32 (2) ◽  
pp. 23
Author(s):  
Ayşe Zeynep Azak ◽  
Murat Tosun ◽  
Melek Masal
Keyword(s):  
Minkowski Space ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Principal Curvatures ◽  
3 Dimensional ◽  
Dimensional Minkowski Space ◽  
Algebraic Invariants ◽  
Distribution Parameters ◽  
Shape Operators ◽  
Necessary And Sufficient

In this paper, null parallel p-equidistant B-scrolls are defined in 3-dimensional Minkowski space  R_1^3 . We prove necessary and sufficient conditions for these B-scrolls to be equivalent of their Cartan frames. The relations between matrices of the shape operators and the algebraic invariants (Gauss, mean curvatures, principal curvatures) of these B-scrolls are shown. Besides we give the relations between second Gauss curvatures, mean curvatures and the distribution parameters of non-developable null parallel p-equidistant B-scrolls. Finally, an example is given related to the null parallel p-equidistant B-scrolls in  R_1^3.

scholarly journals Comparison of Bite Force in Patients After Treatment of Mandibular Fractures With 3-Dimensional Locking Miniplate and Standard Miniplates

2019 ◽  
Vol 1 (1) ◽  
pp. 7-10
Author(s):  
Gaurav Singh ◽  
Madan Mishra ◽  
Amit Gaur ◽  
Dhritiman Pathak
Keyword(s):  
Treatment Strategies ◽  
Bite Force ◽  
Mandibular Fractures ◽  
Time Intervals ◽  
Experimental Conditions ◽  
3 Dimensional ◽  
The Mean ◽  
Group 2 ◽  
Drilling Conditions ◽  
Group 1

Background: Fractures of the mandible can be studied and described in anatomic terms, functional considerations, treatment strategies, and outcome measures. The performance of any fixation system depends on multiple factors including plate adaptation, screw placement, bone quality, drilling conditions, and postoperative patient compliance. Bite force assesses masticatory muscle function under clinical and experimental conditions. Method: 30 patients with isolated, noncomminuted mandibular fractures were randomly divided into two equal groups. Group 1 patients were treated using 3-dimensional locking miniplates and group 2 patients were treated with standard miniplates. The bite forces were recorded at definite time intervals: preoperatively, and second week, sixth week, third month, and sixth month postoperatively. Result: At 6 weeks postoperative, 3 month postoperative, and 6 month postoperative, the mean bite force was found to be significantly higher among group 1 patients as compared to those in group 2 in all the sites. While at 2 week postoperative, the mean bite force was found to be significantly higher in Group 2 as compared to Group 1 at incisor region. Conclusion: The overall results of the present study show better performance in bite force for the 3-dimensional locking miniplate when compared with standard miniplates.

A note on the subcritical generalized age-dependent branching process

1976 ◽  
Vol 13 (4) ◽  
pp. 798-803 ◽  
Author(s):  
R. A. Doney
Keyword(s):  
Branching Process ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Malthusian Parameter ◽  
Age Dependent ◽  
The Mean ◽  
Mean Function ◽  
Necessary And Sufficient

For a subcritical Bellman-Harris process for which the Malthusian parameter α exists and the mean function M(t)∼ aeat as t → ∞, a necessary and sufficient condition for e–at (1 –F(s, t)) to have a non-zero limit is known. The corresponding condition is given for the generalized branching process.

Accuracy of Magnetic Resonance Imaging–Directed Frame-Based Stereotaxis

2011 ◽  
Vol 70 (suppl_1) ◽  
pp. ons114-ons124 ◽  
Author(s):  
Nova B. Thani ◽  
Arul Bala ◽  
Christopher R. P. Lind
Keyword(s):  
Deep Brain Stimulation ◽  
Magnetic Resonance ◽  
Brain Stimulation ◽  
Entry Point ◽  
Mean Deviation ◽  
Guide Tube ◽  
3 Dimensional ◽  
The Mean ◽  
The Brain ◽  
Deep Brain

Abstract BACKGROUND: Accurate placement of a probe to the deep regions of the brain is an important part of neurosurgery. In the modern era, magnetic resonance image (MRI)-based target planning with frame-based stereotaxis is the most common technique. OBJECTIVE: To quantify the inaccuracy in MRI-guided frame-based stereotaxis and to assess the relative contributions of frame movements and MRI distortion. METHODS: The MRI-directed implantable guide-tube technique was used to place carbothane stylettes before implantation of the deep brain stimulation electrodes. The coordinates of target, dural entry point, and other brain landmarks were compared between preoperative and intraoperative MRIs to determine the inaccuracy. RESULTS: The mean 3-dimensional inaccuracy of the stylette at the target was 1.8 mm (95% confidence interval [CI], 1.5-2.1. In deep brain stimulation surgery, the accuracy in the x and y (axial) planes is important; the mean axial inaccuracy was 1.4 mm (95% CI, 1.1-1.8). The maximal mean deviation of the head frame compared with brain over 24.1 ± 1.8 hours was 0.9 mm (95% CI, 0.5-1.1). The mean 3-dimensional inaccuracy of the dural entry point of the stylette was 1.8 mm (95% CI, 1.5-2.1), which is identical to that of the target. CONCLUSION: Stylette positions did deviate from the plan, albeit by 1.4 mm in the axial plane and 1.8 mm in 3-dimensional space. There was no difference between the accuracies at the dura and the target approximately 70 mm deep in the brain, suggesting potential feasibility for accurate planning along the whole trajectory.

scholarly journals New Representations of Spherical Indicatricies of Bertrand Curves in Minkowski 3-Space

Geometry ◽  
2015 ◽  
Vol 2015 ◽  
pp. 1-5
Author(s):  
İsmail Aydemir ◽  
Fırat Yerlikaya
Keyword(s):  
Minkowski Space ◽  
3 Dimensional ◽  
Bertrand Curve ◽  
Dimensional Minkowski Space ◽  
Characteristic Features

We obtained a new representation for timelike Bertrand curves and their Bertrand mate in 3-dimensional Minkowski space. By using this representation, we expressed new representations of spherical indicatricies of Bertrand curves and computed their curvatures and torsions. Furthermore in case the indicatricies of a Bertrand curve are slant helices, we investigated some new characteristic features of these curves.

Characterization of stochastic equilibrium controls by the Malliavin calculus

2021 ◽  
pp. 2150054
Author(s):  
Jiang Yu Nguwi ◽  
Nicolas Privault
Keyword(s):  
Malliavin Calculus ◽  
Linear Quadratic ◽  
Merton Problem ◽  
Classical Duality ◽  
The Mean ◽  
Time Inconsistent ◽  
Necessary And Sufficient ◽  
Mean Variance ◽  
Quadratic Case

We derive a characterization of equilibrium controls in continuous-time, time-inconsistent control (TIC) problems using the Malliavin calculus. For this, the classical duality analysis of adjoint BSDEs is replaced with the Malliavin integration by parts. This results into a necessary and sufficient maximum principle which is applied to a linear-quadratic TIC problem, recovering previous results obtained by duality analysis in the mean-variance case, and extending them to the linear-quadratic setting. We also show that our results apply beyond the linear-quadratic case by treating the generalized Merton problem.

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