In this paper,we show that there exist precisely W(A) Ferrers matrices F(C1,C2,…,cm)such that the rook polynomials is equal to the rook polynomial of Ferrers matrix F(b1,b2,…,bm), where A={b1,b2-1,…,bm-m+1} is a re...In this paper,we show that there exist precisely W(A) Ferrers matrices F(C1,C2,…,cm)such that the rook polynomials is equal to the rook polynomial of Ferrers matrix F(b1,b2,…,bm), where A={b1,b2-1,…,bm-m+1} is a repeated set,W(A) is weight of A.展开更多
For a family of homogeneous Moran sets, where at each level, subintervals are arranged with in-creasing spaces between neighboring subintervals from left to right, we obtained a formula of the Hausdorff dimensions.
Silica mesochannels(SMCs) vertically and regularly oriented to the surface of indium tin oxide(ITO) electrodes were prepared and utilized for preconcentration and detection of methylene blue(MB) in aqueous solution. T...Silica mesochannels(SMCs) vertically and regularly oriented to the surface of indium tin oxide(ITO) electrodes were prepared and utilized for preconcentration and detection of methylene blue(MB) in aqueous solution. The positively charged MB can be adsorbed to the SMCs by following the pseudo-first-order kinetic model. The negative value of ?G=?34.73 k J/mol derived from the Langmuir adsorption isotherm indicated the thermodynamic feasibility of the adsorption and the spontaneous nature of the process. Moreover, the adsorbed MB can undergo an electrochemical reaction on the ITO electrode at a suitable potential and the resulting electrical current can be utilized to quantify the MB in aqueous solution. A good analytical performance for MB with a linear range from 10 nmol/L to 1.0 ?mol/L and a detection limit at the nmol/L level was obtained. We believe that such a platform consisting of SMCs perpendicularly tethered to the underlying electrode surface simultaneously allows enrichment and electrochemical detection and can be extended for the detection of various charged dyes, as well as many other charged species.展开更多
文摘In this paper,we show that there exist precisely W(A) Ferrers matrices F(C1,C2,…,cm)such that the rook polynomials is equal to the rook polynomial of Ferrers matrix F(b1,b2,…,bm), where A={b1,b2-1,…,bm-m+1} is a repeated set,W(A) is weight of A.
文摘For a family of homogeneous Moran sets, where at each level, subintervals are arranged with in-creasing spaces between neighboring subintervals from left to right, we obtained a formula of the Hausdorff dimensions.
基金supported by the National Natural Science Foundation of China(21222504,21335001)the Zhejiang Provincial Natural Science Foundation(R14B050003)+1 种基金the Program for New Century Excellent Talents in Universitythe Fundamental Research Funds for the Central Universities(2014XZZX003-04)
文摘Silica mesochannels(SMCs) vertically and regularly oriented to the surface of indium tin oxide(ITO) electrodes were prepared and utilized for preconcentration and detection of methylene blue(MB) in aqueous solution. The positively charged MB can be adsorbed to the SMCs by following the pseudo-first-order kinetic model. The negative value of ?G=?34.73 k J/mol derived from the Langmuir adsorption isotherm indicated the thermodynamic feasibility of the adsorption and the spontaneous nature of the process. Moreover, the adsorbed MB can undergo an electrochemical reaction on the ITO electrode at a suitable potential and the resulting electrical current can be utilized to quantify the MB in aqueous solution. A good analytical performance for MB with a linear range from 10 nmol/L to 1.0 ?mol/L and a detection limit at the nmol/L level was obtained. We believe that such a platform consisting of SMCs perpendicularly tethered to the underlying electrode surface simultaneously allows enrichment and electrochemical detection and can be extended for the detection of various charged dyes, as well as many other charged species.
