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In this study, we give a new curve pair that generalizes some of the famous pairs of curves as Bertrand and constant torsion curves. This curve pair is defined with the help of a vector obtained by the intersection of the osculating planes such that this vector makes the same angle $\gamma$ with the tangents of the curves. We examine the relations between torsions and curvatures of these curve mates. Also, We have seen that the unit quaternion corresponding to the rotation matrix between the Frenet vectors of the curves is $q=\cos (\theta/2)-\mathbf{i}\sin (\theta/2)\cos \gamma -\mathbf{j}\sin (\theta/2)\sin \gamma$, where $\theta$ is the angle between the reciprocal binormals of the curves. Finally, we show in which specific case which well-known pairs of curves will be obtained.

This study aims at testing the relation between emerging adults’ preference for solitude, social competence, self-esteem on one side and depression on the other side with the mediating role of loneliness. The study group is composed of students that were studying at various faculties at state universities in Turkey in 2019-2020 Academic Year and determined by the easily convenience sampling. 508 students, 279 of whom were female and 229 of whom were male, participated in the study. Data collections tools used in the study are Beck Depression Scale, UCLA Loneliness Scale Short Form, Preference for Solitude Scale, Two-Dimensional Self-Esteem Scale and Perceived Social Competence Scale. The findings of the current study indicate that there is a positive association between depression and loneliness, whereas a negative relationship between loneliness and a tendency for solitude as well as between self-esteem and social competence. Furthermore, the current findings show that loneliness predicts the relation between emerging adults’ preference for solitude, social competence, self-esteem and depression at a statistically significant level.