Let $R$ be a commutative ring and $M$ an $R$-module. A submodule $N$ of is called d-submodule $($resp., fd-submodule$)$ if $\ann_R(m)\subseteq \ann_R(m')$ $\ann_R(F)\subseteq \ann_R(m'))$ for some $m\in N$ finite subset $F\subseteq N)$ $m'\in M$ implies that N.$ Many examples, characterizations, properties these submodules are given. Moreover, we use them to characterize modules satisfying Prop...

SUMMARY We present a tool called MRSD (Metabolic Route Search and Design) to search and design routes based on the weighted compound transform diagraph. The search submodule returns routes between a source and product compound within seconds in the network of one or multiple organisms based on data from KEGG. The design submodule designs a route from an appointed compound in an interactive mode...

PURPOSE The clinical outcome for patients with breast cancer is influenced by the metastatic competence of the cancer and its sensitivity to endocrine therapy and chemotherapy. A molecular marker may be prognostic of outcome or predictive of response to therapy, or a combination of both. EXPERIMENTAL DESIGN We examined separately the prognostic and predictive values of tau mRNA expression in ...

A new submodule clustering method via sparse and lowrank representation for multi-way data is proposed in this paper. Instead of reshaping multi-way data into vectors, this method maintains their natural orders to preserve data intrinsic structures, e.g., image data kept as matrices. To implement clustering, the multi-way data, viewed as tensors, are represented by the proposed tensor sparse an...

Abstract I present a method for estimating the fidelity F ( μ , τ ) between preparable quantum state and classically specified pure target $$\tau =\left|\tau \right\rangle \left\langle \tau \right|$$ τ = using simple circuits on-the-fly clas...

Alzheimer disease is a major cause of cognitive failure, and a pathogenically related but more subtle process accounts for many cases of mild memory symptoms in older humans. Insoluble fibrillar plaques of amyloid β-proteins (Aβ) and neurofibrillary deposits of hyperphosphorylated tau proteins are the diagnostic lesions of AD, but their temporal mechanistic relationship has long been debated. T...

Alzheimer disease is a major cause of cognitive failure, and a pathogenically related but more subtle process accounts for many cases of mildmemory symptoms in older humans. Insoluble fibrillar plaques of amyloid β-proteins (Aβ) and neurofibrillary deposits of hyperphosphorylated tau proteins are the diagnostic lesions of AD, but their temporal mechanistic relationship has long been debated. Th...

‎Let $R$ be a domain with quotiont field $K$‎, ‎and‎ ‎let $N$ be a submodule of an $R$-module $M$‎. ‎We say that $N$ is‎ ‎powerful (strongly primary) if $x,yin K$ and‎ ‎$xyMsubseteq N$‎, ‎then $xin R$ or $yin R$ ($xMsubseteq N$‎ ‎or $y^nMsubseteq N$ for some $ngeq1$)‎. ‎We show that a submodule‎ ‎with either of these properties is comparable to every prime‎ ‎submodule of $M$‎, ‎also we show tha...

‎In this work‎, ‎we introduce the concept of classical 2-absorbing secondary modules over a commutative ring as a generalization of secondary modules and investigate some basic properties of this class of modules‎. ‎Let $R$ be a commutative ring with‎ ‎identity‎. ‎We say that a non-zero submodule $N$ of an $R$-module $M$ is a‎ ‎emph{classical 2-absorbing secondary submodule} of $M$ ...