In this paper a numerical method to compute principal component geodesics for Kendall’s planar shape spaces which are essentially complex projective spaces is presented. Underlying is the notion of principal component analysis based on geodesics for non-Euclidean manifolds as proposed in an earlier paper by Huckemann and Ziezold (2006). Currently, principal component analysis for shape spaces i...

This paper studies the usefulness of the projective approach to structure from motion (SFM). We conduct an essentially algorithm{independent experimental comparison of projective versus Euclidean reconstruction. Our results show that Euclidean reconstruction is essentially as accurate as pro-jective reconstruction, even with signiicant calibration error and for the pure projective structure. Th...

We proved in Theorem 3. 15 b that free modules have the precise same property that. projective modules 2 attributes to projective modules. In fact, it is easy to use.BIG PROJECTIVE MODULES ARE FREE. Finitely generated proiective modules rise significantly in certain geometric nd.dorff space X and finitely generated projective modules over the ring of continuous real-valued functions on X. A num...

.Mmtract. In thL~ paper the first infinite series of translation nets with nonabelian translation groups and a large number of parallel classes are constructed. For that purpose we investigate partial congruence partitions (PCPs) with at least one normal component. Two series correspond to partial congruence partitions containing one normal elementary abelian component. The construction results...

In this paper, we study the left orthogonal class of max-flat modules which are homological objects related to s-pure exact sequences and module homomorphisms. Namely, a right $A$ is called MF-projective if ${Ext}^{1}_{R}(A,B)=0$ for any $R$-module $B$, strongly ${Ext}^{i}_{R}(A,B)=0$ all $R$-modules $B$ $i\geq 1$. Firstly, give some properties $MF$-projective SMF-projective modules. Then intro...

Projective texture mapping is used to project a texture map onto scene geometry. It has been used in many applications, since it eliminates the assignment of fixed texture coordinates and provides a good method of representing synthetic images or photographs in image-based rendering. But conventional projective texture mapping has limitations in the field of view and the degree of navigation be...

This paper is a continuation of the papers J. Pure Appl. Algebra, 210 (2007), 437–445 and J. Algebra Appl., 8 (2009), 219–227. Namely, we introduce and study a doubly filtered set of classes of modules of finite Gorenstein projective dimension, which are called (n, m)-strongly Gorenstein projective ((n, m)-SG-projective for short) for integers n ≥ 1 and m ≥ 0. We are mainly interested in studyi...

Let K = Fq be a finite field. We introduce a family of projective Reed-Muller-type codes called projective Segre codes. Using commutative algebra and linear algebra methods, we study their basic parameters and show that they are direct products of projective Reed-Mullertype codes. As a consequence we recover some results on projective Reed-Muller-type codes over the Segre variety and over proje...

The non-split extension group $overline{G} = 5^3{^.}L(3,5)$ is a subgroup of order 46500000 and of index 1113229656 in Ly. The group $overline{G}$ in turn has L(3,5) and $5^2{:}2.A_5$ as inertia factors. The group $5^2{:}2.A_5$ is of order 3 000 and is of index 124 in L(3,5). The aim of this paper is to compute the Fischer-Clifford matrices of $overline{G}$, which together with associated parti...

1.1 Statement and Context. One of the underlying principles in the study of Kleinian groups is that aspects of the complex projective geometry of quotients of Ĉ by the groups reflect properties of the threedimensional hyperbolic geometry of the quotients of H by the groups. Yet, even though it has been over thirty-five years since Lipman Bers wrote down a holomorphic embedding of the Teichmülle...