The main purpose of Phase Impenetrability Condition, and the whole Phase Theory itself, is to predict the movement path of linguistic structures. In this article, in the first place, the movement path of subject within a sentence will be studied and it is argued that subject moves through the edge of vP and then goes to the specifier of tense group. However, contrary to subject movement, the movement of ‘ ra’ object and ‘ non-ra’ object and ‘ non-verbal part of a compound verb show no sign that these syntactic structures move through the edge of vP. Regarding the complement preposition phrase, it is argued that having moved out, this syntactic structure which aimed at going to topic group or focus group, moves through the edge of vP and receives ‘ ra’ which is a functional marker. According to the data of the article and according to the geodesic (Donkey Hypothesis), it is claimed that there is no absolute minimalism in linguistics like absolute synonymy.

In this paper we discuss some results related to angle between geodesic segments in an infinite dimensional and an asymptotic Teichm¨uller space. Also, we construct a geodesic triangle in Universal Teichm¨uller space and calculate all of its interior angles

In this paper, we present some common fixed point theorems for two generalized nonexpansive multivalued mappings in CAT (0) spaces as well as in UCED Banach spaces. Moreover, we prove the existence of fixed points for generalized nonexpansive multivalued mappings in complete geodesic metric spaces with con- vex metric for which the asymptotic center of a bounded sequence in a bounded closed convex subset is nonempty and singleton. The results obtained in this paper extend and improve some recent results.

In this paper, a novel Patch geodesic Derivative Pattern (PGDP) describing the texture map of a face through its shape data is proposed. geodesic adjusted textures are encoded into derivative patterns for similarity measurement between two 3D images with different pose and expression variations. An extensive experimental investigation is conducted using the publicly available Bosphorus and BU-3DFE databases covering face recognition under pose and expression changes. The performance of the proposed method is compared with the performance of the state-of-the-art benchmark approaches. The encouraging experimental results demonstrate that the proposed method is a new solution for 3D face recognition in single model databases.

In image inpainting, distorted and damaged parts of image or selected objects are removed or replaced with the appropriate information. In this article, image inpainting is performed by using frequency information of wavelet transform. The fill-in is done by diffusion of information of intact pixels into the damaged regions, which is begun from the outermost pixels and gradually the damaged region is reconstructed. To determine direction and the amount of diffusion, the geodesic path based image inpainting method is generalized by incorporating information of wavelet domain. The experimental results confirm superiority of the proposed method over the geodesic path based image inpainting method.

In this paper, we consider invariant (α, β)-metrics and describe all geodesic vectors and investigate the set of all homogeneous geodesics on left invariant hypercomplex four dimensional simply connected Lie groups. Also, we study the conditions for the Douglas and Berwald type of (α, β)-metrics on the left invariant hypercomplex four dimensional simply connected Lie groups.