The Hyperbolic Spinor Representation of Transformations in R-1(3) by Means of Split Quaternions

In this study, firstly, we give a different approach to the relationship between the split quaternions and rotations in Minkowski space R-1(3). In addition, we obtain an automorphism of the split quaternion algebra H' corresponding to a rotation in R-1(3). Then, we give the relationship between the hyperbolic spinors and rotations in R-1(3). Finally, we associate to a split quaternion with a hyperbolic spinor by means of a transformation. In this way, we show that the rotation of a rigid body in the Minkowski 3-space R-1(3) expressed the split quaternions can be written by means of the hyperbolic spinors with two hyperbolic components. So, we obtain a new and short representation (hyperbolic spinor representation) of transformation in the 3-dimensional Minkowski space R-1(3) expressed by means of split quaternions

The effect of different anti-inflammatory treatment strategies on process of atherosclerosis in ankylosing spondylitis patients

Our aim in this study was to examine the effects of different anti-inflammatory treatment strategies on the process of atherosclerosis, which is an important cause of mortality in ankylosing spondylitis (AS) patients, by examining the possible effect of treatments on inflammation, lipid profile and oxidative stress parameters in patients with AS