arXiv subjects
Publications and source records attributed to M. Rahmani.
In this paper we intend to introduce the concept of c-K-g-frames, which are the generalization of K-g-frames. In addition, we prove some new results on c-K-g-frames on Hilbert spaces. Moreover, we define the related oprators of c-K-g frames. Then, we give necessary and sufficient conditions on c-K-frames to characterize them. Finally, we verify perturbation of c-K-g-frames.
Let $(R, \mathfrak{m})$ be a Noetherian local ring. In this paper, we introduce a dual notion for dualizing modules, namely codualizing modules. We study the basic properties of codualizing modules and use them to establish an equivalence between the category of noetherian modules of finite projective dimension and the category of artinian modules of finite projective dimension. Next, we give some applications of codualizing modules. Finally, we present a mixed identity involving quasidualizing module that characterize the codualizing module. As an application, we obtain a necessary and sufficient condition for $R$ to be Gorenstein.
Let $R$ be a Noetherian ring and let $C$ be a semidualizing $R$-module. In this paper, by using relative homological dimensions with respect to $C$, we impose various conditions on $C$ to be dualizing. First, we show that $C$ is dualizing if and only if there exists a Cohen-Macaulay $R$-module of type 1 and of finite G$ _C $-dimension. This result extends Takahashi \cite[Theorem 2.3]{T} as well as Christensen \cite[Proposition 8.4]{C}. Next, as a generalization of Xu \cite[Theorem 3.2]{X2}, we show that $C$ is dualizing if and only if for an $R$-module $M$, the necessary and sufficient condition for $M$ to be $C$-injective is that $ π_i(\fp , M) = 0 $ for all $ \fp \in \Spec(R) $ and all $ i \neq \h(\fp) $, where $ π_i $ is the invariant dual to the Bass numbers defined by E.Enochs and J.Xu \cite{EX}. We use the later result to give an explicit structure of the minimal flat resolution of $ \H_{\fm}^d(R) $, where $ (R, \fm) $ is a $ d $-dimensional Cohen-Macaulay local ring possessing a canonical module. As an application, we compute the torsion product of these local cohomology modules.
Let $R$ be a Noetherian ring and let $C$ be a semidualizing $R$-module. In this paper, by using the classes $ \mathcal{P}_C $ and $ \mathcal{I}_C $, we extend the notions of perfect and coperfect modules introduced by D.Rees \cite{R} and O.Jenda \cite{J1}. First, we study the basic properties of these modules and relations between them. Next, we characterize local rings in terms of the existence of special perfect (resp. coperfect) modules.
Let $R$ be a Noetherian ring and let $C$ be a semidualizing $R$-module. In this paper, by using the semidualizing modules, we define and study new classes of modules and homological dimensions and investigate the relations between them. In parallel, we obtain some necessary and sufficient condition for $ C $ to be dualizing.
Attosecond streaking of photoelectrons emitted by extreme ultraviolet light has begun to reveal how electrons behave during their transport within simple crystalline solids. Many sample types within nanoplasmonics, thin-film physics, and semiconductor physics, however, do not have a simple single crystal structure. The electron dynamics which underpin the optical response of plasmonic nanostructures and wide-bandgap semiconductors happen on an attosecond timescale. Measuring these dynamics using attosecond streaking will enable such systems to be specially tailored for applications in areas such as ultrafast opto-electronics. We show that streaking can be extended to this very general type of sample by presenting streaking measurements on an amorphous film of the wide-bandgap semiconductor tungsten trioxide, and on polycrystalline gold, a material that forms the basis of many nanoplasmonic devices. Our measurements reveal the near-field temporal structure at the sample surface, and photoelectron wavepacket temporal broadening consistent with a spread of electron transport times to the surface.