With the aid of Mullin-Rota's substitution rule, we show that the Sheffertype differential operators together with the delta operators ? and D could be used to construct a pair of expansion formulas that imply a w...With the aid of Mullin-Rota's substitution rule, we show that the Sheffertype differential operators together with the delta operators ? and D could be used to construct a pair of expansion formulas that imply a wide variety of summation formulas in the discrete analysis and combinatorics. A convergence theorem is established for a fruitful source formula that implies more than 20 noted classical fomulas and identities as consequences. Numerous new formulas are also presented as illustrative examples. Finally, it is shown that a kind of lifting process can be used to produce certain chains of(∞~m) degree formulas for m ≥ 3 with m ≡ 1(mod 2) and m ≡ 1(mod 3), respectively.展开更多
In this paper, ternary Co-Pt-P thin films were prepared by Co-P chips pasted on the cobalt target. The structure magnetron sputtering with platinum and home-made and magnetic properties were investigated by X-ray diff...In this paper, ternary Co-Pt-P thin films were prepared by Co-P chips pasted on the cobalt target. The structure magnetron sputtering with platinum and home-made and magnetic properties were investigated by X-ray diffraction （XRD） and vibrating sample magnetometer （VSM）, respectively. With increasing phosphor content, the coercivities of Co-12 at.% Pt-P films increase from 1034 to 1525 Oe owing to the exchange decoupling among magnetic grains. The decrease of inter-granular exchange coupling was confirmed by delta-M curve measurement and magnetic force microscopy （MFM）. Transmission electronic microscopy （TEM） with nano- beam composition analysis shows that phosphor segregated at cobalt-based grain boundaries is responsible for the exchange decoupling. It is thus suggested that the phosphor addition is effective to tune the exchange coupling of magnetic grains, particularly for perpendicular recording media.展开更多
文摘With the aid of Mullin-Rota's substitution rule, we show that the Sheffertype differential operators together with the delta operators ? and D could be used to construct a pair of expansion formulas that imply a wide variety of summation formulas in the discrete analysis and combinatorics. A convergence theorem is established for a fruitful source formula that implies more than 20 noted classical fomulas and identities as consequences. Numerous new formulas are also presented as illustrative examples. Finally, it is shown that a kind of lifting process can be used to produce certain chains of(∞~m) degree formulas for m ≥ 3 with m ≡ 1(mod 2) and m ≡ 1(mod 3), respectively.
基金supported by the Program for New Century Excellent Talents in University (No. NCET-09-0272)the Liaoning Program for Excellent Talents in University (No. 2009R23)One of authors, B. Yang appreciates Northeastern University Research Foundation for Excellent Doctor Candidates (No. 200904)
文摘In this paper, ternary Co-Pt-P thin films were prepared by Co-P chips pasted on the cobalt target. The structure magnetron sputtering with platinum and home-made and magnetic properties were investigated by X-ray diffraction （XRD） and vibrating sample magnetometer （VSM）, respectively. With increasing phosphor content, the coercivities of Co-12 at.% Pt-P films increase from 1034 to 1525 Oe owing to the exchange decoupling among magnetic grains. The decrease of inter-granular exchange coupling was confirmed by delta-M curve measurement and magnetic force microscopy （MFM）. Transmission electronic microscopy （TEM） with nano- beam composition analysis shows that phosphor segregated at cobalt-based grain boundaries is responsible for the exchange decoupling. It is thus suggested that the phosphor addition is effective to tune the exchange coupling of magnetic grains, particularly for perpendicular recording media.
