Throughout this paper, R will denote a commutative ring with identity and M is a unitary R- module and Z will denote the ring of integers. We introduce the graph Ω(M) of module M with the set of vertices contain all nontrivial non-essential submodules of M. We investigate the interplay between graph-theoretic properties of Ω(M) and algebraic properties of M. Also, we assign the values of natura...

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This paper investigates the complexity of the min-max and min-max regret assignment problems both in the discrete scenario and interval data cases. We show that these problems are strongly NP -hard for an unbounded number of scenarios. We also show that the interval data min-max regret assignment problem is strongly NP -hard.

beta subunits (Ca(v)beta) increase macroscopic currents of voltage-dependent Ca2+ channels (VDCC) by increasing surface expression and modulating their gating, causing a leftward shift in conductance-voltage (G-V) curve and increasing the maximal open probability, P(o,max). In L-type Ca(v)1.2 channels, the Ca(v)beta-induced increase in macroscopic current crucially depends on the initial segmen...

The noncentrosymmetric nature of single-layer (SL) transition-metal dichalcogenides (TMD) manifests itself in the finite piezoelectricity and valley-Zeeman coupling. We microscopically model nonlinear exciton transport nanobubbles SL TMDs. Thanks to giant piezoelectric effect, we obtain an enormous internal electric field, ${E}_{\mathrm{piezo}}\ensuremath{\sim}{10}^{7}\phantom{\rule{0.16em}{0ex...

Article history: Received 21 September 2009 Received in revised form 23 August 2010 Accepted 23 August 2010 Available online 8 September 2010 Recent years have witnessed an increased interest in computing cosine similarity in many application domains. Most previous studies require the specification of a minimum similarity threshold to perform the cosine similarity computation. However, it is us...