In this paper, we study geometry of mappings of spatial kinematics in Lorentzian space with the aid of dual number and split quaternion. Also, we give orthogonal rotation matrix A with respect to the Lorentzian Rodrigues parameters and the Lorentzian Euler parameters in such a space. Then, Study's soma is developed and used to define the mapping of spatial kinematics into points of a dual Lorentzian projective space.
Lorentz Uzayında Uzaysal Kinematiklerin Geometrisi Üzerine Bir ÇalışmaAnahtar Kelimeler Dual sayı, Euler parametreleri, Lorentz uzay, Uzaysal kinematik, Split kuaterniyon Özet: Bu çalışmada, dual sayı ve split kuaterniyon yardımıyla Lorentz uzayında uzaysal kinematiklerin dönüşümlerinin geometrisi ele alınmıştır. Ayrıca, bu uzayda bir A ortogonal dönüşüm matrisi, Lorentziyen Rodrigues ve Euler parametrelerine göre verilmiştir. Son olarak, Study'nin "soma" olarak isimlendirdigi dönüşüm uzayı geliştirilmiş ve bu yapı bir dual Lorentz projektif uzayın noktaları içinde uzaysal kinematiklerin dönüşümünü tanımlamak için kullanılmıştır.
We study magnetic trajectories in Lie groups equipped with bi‐invariant Riemannian metric. We define the Lorentz force of a magnetic field in a Lie group G, and then, we give the Lorentz force equation for the associated magnetic trajectories that are curves in G. When the manifold is a Lie group G equipped with bi‐invariant Riemannian metric, we derive differential equation system that characterizes magnetic flow associated with the Killing magnetic curves with regard to the Lie reduction of the curve γ in G.
In the present paper, the geometrical instantaneous invariants of the motion H m /H f in dual Lorentzian 3 -space are determined. Depending on this, the dual Lorentzian instantaneous screw axis of the motion of K m with respect to the dual pseudohyperbolic space K m is constructed. On the other hand, we show that, in each position of H m , the fixed and moving axodes have the instantaneous screw axis of this position in common. We also give relations between the geodetic curvature and the curvature of the polodes.
The financial ratio analysis is an important issue for the stock exchange markets which have many sub-sectoral indexes. During Industry 4.0 revolution and transition, the sector of information and technology is shown as one of the sectors that have great strategic importance in the global change and development process. So, the performance of the information and technology sector provides a significant added value to the economies. In this study, multi-criteria decision-making (MCDM) approaches will be used to determine the weights of the criteria with considering the experts' opinions used in the evaluation of the financial performance of the companies operating in the field of Information and Technology Sector of BIST Stock Index (XUTEK). In order to measure the financial performance of companies with MCDM methods, the ratios of the liquidity, operational/activity, financial structure, and profitability are obtained from the financial statements are frequently applied in the scientific literature. In the study, criteria weights were determined by using the pairwise comparison feature of the analytical hierarchy process method and expert opinions. Then, the smallest and largest values of the financial ratio values in quarterly periods in 2020 and the uncertainty formed were evaluated with the gray relational analysis method. After all; XUTEK stocks to be included in the priority investment portfolio in terms of financial performance have been determined.
This paper deals with rectifying curves and their characterization in arbitrary dimensional Lorentz n-space. Considering the structure of a rectifying curve, we give some generalizations of such curves in Lorentz n-space. Moreover, we characterize and prove some properties of these curves in terms of their curvature functions.
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