let $r$ be a commutative ring with identity and $m$ be a finitely generated unital $r$-module. in this paper, first we give necessary and sufficient conditions that a finitely generated module to be a multiplication module. moreover, we investigate some conditions which imply that the module $m$ is the direct sum of some cyclic modules and free modules. then some properties of fitting ideals of...

We show  that a projective maximal submodule of afinitely generated, regular, extending module is a directsummand. Hence, every finitely generated, regular, extendingmodule with projective maximal submodules is semisimple. As aconsequence, we observe that every regular, hereditary, extendingmodule is semisimple. This generalizes and simplifies a result of  Dung and   Smith. As another consequen...

This paper presents a vision-based method to estimate the *real motion of a single camera from views of a planar patch. Projective techniques allow to estimate camera motion from pixel space apparent motion without explicit 3-D reconstruction. In addition, the paper will present the HELINSPEC project, the framework where the proposed method has been tested, and will detail some applications in ...

we show  that a projective maximal submodule of afinitely generated, regular, extending module is a directsummand. hence, every finitely generated, regular, extendingmodule with projective maximal submodules is semisimple. as aconsequence, we observe that every regular, hereditary, extendingmodule is semisimple. this generalizes and simplifies a result of  dung and   smith. as another consequen...

The past decade has seen considerable advances in the application of principles from projective geometry to problems in image analysis and computer vision. In this paper, we review a subset of this work, and leverage these results for the purpose of forensic analysis. Specifically, we review three techniques for making metric measurements on planar surfaces from a single image. The resulting te...

In this paper, by considering the notion of extended BCK-module, we define the concepts of free extended BCK-module, free object in category of extended BCK-modules and we state and prove some related results. Specially, we define the notion of idempotent extended BCK-module and we get some important results in free extended BCK-modules. In particular, in category of idempotent extended BCK-mod...

We propose scveral new techniques for mosaic-ing images of Japanese picture scrolls. Previous methods cannot accurately stitch these images, because they are too wide. To solve this problem , we propose three techniques that can stitch without any seams. The first technique adjusts its height of each image in advance. The second technique uses planar projective transformation among three images...