Investigating generalized quaternions with dual-generalized complex numbers

summary:We aim to introduce generalized quaternions with dual-generalized complex number coefficients for all real values $\alpha$, $\beta$ and $\mathfrak {p}$. Furthermore, the algebraic structures, properties and matrix forms are expressed as generalized quaternions and dual-generalized complex numbers. Finally, based on their matrix representations, the multiplication of these quaternions is restated and numerical examples are given

A Geometric Aspect of the Two-Parameter Planar Lorentzian Motions

We examined the moving coordinate systems, the polar axes, the density invariance of the polar axis transformation, and the curve plotter points and the support function of the two-parameter planar Lorentzian motion. Furthermore, we were concerned with the determination of the motion using the polar axes and analyzed the motion when the density of the polar axes is zero

On ruled non-degenerate surfaces with Darboux frame in Minkowski 3-space

In this paper, ruled non-degenerate surfaces with respect to Darboux frame are studied. Characterization of them which are related to the geodesic torsion, the normal curvature and the geodesic curvature with respect to Darboux frame are examined. Furthermore, some special cases of non-null rulings are demonstrated according to Frenet frame {T, N, B} with Darboux frame {T, g, n}. Finally, the integral invariants of these surfaces are examined.The first author has been partially supported by TUBITAK (2211-Domestic PhD Scholarship) The Scientific and Technological Research Council of Turkey.Publisher's Versio

How to reduce stress on the pedicle screws in thoracic spine? Importance of screw trajectory: A finite element analysis

WOS: 000454722700004PubMed ID: 29368324AIM: To investigate the biomechanical comparison of thoracic transpedicular screw trajectories on the sagittal plane. MATERIAL and METHODS: A three-dimensional, non-linear finite element analysis (FEA) model of T8 through T9 was used. Anatomic trajectory (AT) and Straightforward trajectory (ST) models of the transpedicular screws were used in the intact FEA model. The von-Mises stress and range of motion (ROM) of the transpedicular screws were evaluated. RESULTS: The difference in ROM between both techniques was negligible. In lateral bending and axial rotation, FEA showed decrease in stress by 25% and 8%, respectively, when pedicle screws were placed using AT. CONCLUSION: AT decreased the von-Mises stress of the pedicle screws, thereby reducing the rates of screw breakage and fatigue risks. In addition, we believe that AT could protect against screw loosening because the von-Mises stress of the internal fixation was scattered.Turkish Neurosurgical SocietyPreparation for publication of this article is partly supported by the Turkish Neurosurgical Society

Complications of 2-level dynamic stabilization: A correlative clinical and radiological analysis at two-year follow-up on 103 patients

WOS: 000443444000010PubMed ID: 30192368AIM: To investigate the postoperative complications, such as screw loosening, screw breakage and adjacent segment disease (ASD), in patients who underwent surgery with 2-level dynamic stabilization systems. MATERIAL and METHODS: Postoperative complications, clinical improvements and radiological parameters in patients who underwent surgery using a dynamic system for 2-level lumbar stabilization were retrospectively reviewed. A total of 103 patients with lumbar degenerative spinal instability underwent 2-level dynamic stabilization. Clinical findings were reviewed at 2-year follow-up. Screw breakage and loosening were evaluated during this duration together with clinical findings. RESULTS: Visual analog scale (VAS) and Oswestry Disability Index (ODI) scores were significantly decreased at the four-month evaluation, and they were also decreased at the 1-year follow up and at the 24th postoperative month. ASD was diagnosed in twelve (8 females, 4 males) of the 103 patients in the follow-up radiological and clinical controls. There were 9 screw breakages and 4 screw loosening cases. The complication rate of 2-level dynamic stabilization was high in this study. CONCLUSION: Our results showed that complications (screw loosening or breakage and adjacent segment disease) are not rare after 2-level dynamic stabilization, unlike the acceptable results with the single-level dynamic system. The most probable explanation is that the instrument system behaves more rigidly with every additional segment

Radyological Comparison of Lumbar Nerve Root Thickness in Patients with Lumbar Disc Herniation

Abstract Introduction: the aim of this study was to compare radiologically the effect of the disc on Root thicknesses in patients with acute disc herniation. Methods: It was performed by measuring the same level of Root thickness in lumbar MRI images of patients presenting with acute disc herniation symptoms. Findings: Lumbar MRI images of 95 patients were compared radiologically. It was statistically determined that the thickness of the nerve root on the side exposed to the compression of acute disc herniation increased compared to the other nerve root thickness at the same level. Results: This study found statistically significant increase in the diameter of the affected nerve root in acute lumbar disc herniation. Especially in multi-level disc herniations, it may be useful to measure the nerve root thickness in determining the level that causes the actual clinic

Effects of Resveratrol on Inflammation and Apoptosis After Experimental Spinal Cord Injury

AIM: To determine the effects of resveratrol on inflammation and apoptosis after experimental spinal cord injury (SCI)