We study Serre’s condition (Sn) for tensor products of modules over a commutative noetherian local ring R. Specifically, we consider the following question. For finitely generated R-modules M and N, either which is (n+1)-Tor-rigid, if product M⊗RN satisfies (Sn+1), then does ToriR(M,N)=0 hold all i≥1? The aim this paper to give an affirmative answer question assume freeness on modules. As appli...

We introduce the notion of mutation on the set of n-cluster tilting subcategories in a triangulated category with Auslander-Reiten-Serre duality. Using this idea, we are able to obtain the complete classifications of rigid Cohen-Macaulay modules over certain Veronese subrings.

We compute the representation-theoretic rank of a finite dimensional quasi-Hopf algebra H and of its quantum double D(H), within the rigid braided category of finite dimensional left D(H)-modules.

We consider stacks of filtered φ-modules over rigid analytic spaces and adic spaces. We show that these modules parametrize p-adic Galois representations of the absolute Galois group of a p-adic field with varying coefficients over an open substack containing all classical points. Further we study a period morphism (defined by Pappas and Rapoport) from a stack parametrising integral data and de...

in this paper, we propose a novel method for fully automatic detection and tracking of human heads and faces in video sequences. the proposed algorithm consists of two modules: a face detection module and a face tracking module. the detection module, detects the face region and approximates it with an ellipse at the first frame using a modified version of adaboost cascaded classifier. the detec...

the concepts of free modules, projective modules, injective modules and the likeform an important area in module theory. the notion of free fuzzy modules was introducedby muganda as an extension of free modules in the fuzzy context. zahedi and ameriintroduced the concept of projective and injective l-modules. in this paper we give analternate definition for projective l-modules. we prove that e...

an r-module m is called strongly noncosingular if it has no nonzero rad-small (cosingular) homomorphic image in the sense of harada. it is proven that (1) an r-module m is strongly noncosingular if and only if m is coatomic and noncosingular; (2) a right perfect ring r is artinian hereditary serial if and only if the class of injective modules coincides with the class of (strongly) noncosingula...

This report details the actual concrete architecture of Firefox; specifically the JavaScript interpreter, the XML parser and display backend components. The architecture extracted from the code did not follow the rigid boundaries of the conceptual architecture. After some investigation code modules were grouped together to try and recreate the conceptual layers. This was a difficult task becaus...

1 Motivation Over the years of human history, man-made systems reached higher and higher levels of complexity, as we wanted them to perform more and more complicated tasks. The predominant way humans use to build their machines is to construct them as more or less rigid structures of modules, each performing a predeened task, with a minimal number of connections between modules. In fact, this m...