Let be a simple graph with vertex set and edge set . Let have at least vertices of degree at least , where and are positive integers. A function is said to be a signed -edge cover of if for at least vertices of , wher...Let be a simple graph with vertex set and edge set . Let have at least vertices of degree at least , where and are positive integers. A function is said to be a signed -edge cover of if for at least vertices of , where . The value , taking over all signed -edge covers of is called the signed -edge cover number of and denoted by . In this paper we give some bounds on the signed -edge cover number of graphs.展开更多
It is shown that the lower bound on the maximum genus of a 3-edge connected loopless graph is at least one-third of its cycle rank. Moreover, this lower bound is tight. There are infinitely such graphs attaining the b...It is shown that the lower bound on the maximum genus of a 3-edge connected loopless graph is at least one-third of its cycle rank. Moreover, this lower bound is tight. There are infinitely such graphs attaining the bound.展开更多
Rhenium is a very scarce element, occurring in the Earth's crust mainly carried by molybdenite (MoS2). Due to a very low availability comparative to actual industrial demand, rhenium is nowadays one of the most ex...Rhenium is a very scarce element, occurring in the Earth's crust mainly carried by molybdenite (MoS2). Due to a very low availability comparative to actual industrial demand, rhenium is nowadays one of the most expensive mineral commodities and an increased interest is focused on ex- ploring residues resulting from a long-term mining, particularly of sulphide ore deposits. It is therefore noteworthy to assign the presence of rhenium (in a concentration up to 3 ppm) in the waste materials from the old sulphur factory at the abandoned mine of Sao Domingos (Iberian Pyrite Belt, Southeast Portugal), exploited since the Roman occupation of Iberia. Aiming at a potential sustainable recovery of rhenium as a by-product, X-ray near-edge absorption spectroscopy (XANES) was applied to clarify the Re-binding and mode of occurrence by comparing Re L3-edge XANES spectra obtained from mine waste samples (previously fully characterized by X-ray laboratory techniques) with similar spectra collected from Re-rich molybdenites (Mo1-xRexS2) and from Re-O model compounds configuring various valences and coordination environments of rhenium ions. Obtained results are commented, ruling out a possible Re-S binding and rather conforming with the binding of rhenium to oxygen in the analysed mine waste materials.展开更多
文摘Let be a simple graph with vertex set and edge set . Let have at least vertices of degree at least , where and are positive integers. A function is said to be a signed -edge cover of if for at least vertices of , where . The value , taking over all signed -edge covers of is called the signed -edge cover number of and denoted by . In this paper we give some bounds on the signed -edge cover number of graphs.
文摘It is shown that the lower bound on the maximum genus of a 3-edge connected loopless graph is at least one-third of its cycle rank. Moreover, this lower bound is tight. There are infinitely such graphs attaining the bound.
基金the project MinReMol(Ref.EXPL/AAG-REC/0978/2012),financed by FEDER Funds through the Operational Program on Competitive Factors(COMPETE:FCOMP-01-0124-FEDER-027516)by national funds through the Portuguese Foundation for Science and Technology(FCT-MCTES)support of FCT-MCTES through the Strategic Project LA25-2011-2012(ref.PEst-C/CTM/LA0025/2011).
文摘Rhenium is a very scarce element, occurring in the Earth's crust mainly carried by molybdenite (MoS2). Due to a very low availability comparative to actual industrial demand, rhenium is nowadays one of the most expensive mineral commodities and an increased interest is focused on ex- ploring residues resulting from a long-term mining, particularly of sulphide ore deposits. It is therefore noteworthy to assign the presence of rhenium (in a concentration up to 3 ppm) in the waste materials from the old sulphur factory at the abandoned mine of Sao Domingos (Iberian Pyrite Belt, Southeast Portugal), exploited since the Roman occupation of Iberia. Aiming at a potential sustainable recovery of rhenium as a by-product, X-ray near-edge absorption spectroscopy (XANES) was applied to clarify the Re-binding and mode of occurrence by comparing Re L3-edge XANES spectra obtained from mine waste samples (previously fully characterized by X-ray laboratory techniques) with similar spectra collected from Re-rich molybdenites (Mo1-xRexS2) and from Re-O model compounds configuring various valences and coordination environments of rhenium ions. Obtained results are commented, ruling out a possible Re-S binding and rather conforming with the binding of rhenium to oxygen in the analysed mine waste materials.
