A new method called spline convolution (SC) for resolving overlapped peaks was proposed in this paper. The differential pulse voltammetric overlapped peaks of mixtures of Pb(II) and Tl(I) were investigated by this me...A new method called spline convolution (SC) for resolving overlapped peaks was proposed in this paper. The differential pulse voltammetric overlapped peaks of mixtures of Pb(II) and Tl(I) were investigated by this method, and satisfactory results were obtained. The results show excellent correlation between peak areas of the processed signals and the concentrations.展开更多
If an operator is not invertible, we are interested if there is a subspace such that the reduction of the operator to that subspace is invertible. In this paper we give a spectral approach to generalized inverses cons...If an operator is not invertible, we are interested if there is a subspace such that the reduction of the operator to that subspace is invertible. In this paper we give a spectral approach to generalized inverses considering the subspace determined by the range of the spectral projection associated with an operator and a spectral set containing the point 0. We compare the cases, 0 is a simple pole of the resolvent function, 0 is a pole of order n of the resolvent function, 0 is an isolated point of the spectrum, and 0 is contained in a circularly isolated spectral set.展开更多
For a connected graph G with vertex set V,let RG{x,y}={z∈V:dG(x,z)≠dG(y,z)}for any distinct x,y∈V,where dG(u,w)denotes the length of a shortest uw-path in G.For a real-valued function g defined on V,let g(V)=∑s∈V...For a connected graph G with vertex set V,let RG{x,y}={z∈V:dG(x,z)≠dG(y,z)}for any distinct x,y∈V,where dG(u,w)denotes the length of a shortest uw-path in G.For a real-valued function g defined on V,let g(V)=∑s∈V g(s).Let C={G_(1),G_(2),...,G_(k)}be a family of connected graphs having a common vertex set V,where k≥2 and|V|≥3.A real-valued function h:V→[0,1]is a simultaneous resolving function of C if h(RG{x,y})≥1 for any distinct vertices x,y∈V and for every graph G∈C.The simultaneous fractional dimension,Sdf(C),of C is min{h(V):h is a simultaneous resolving function of C}.In this paper,we initiate the study of the simultaneous fractional dimension of a graph family.We obtain max1≤i≤k{dimf(Gi)}≤Sd_(f)(C)≤min{∑k i=1 dimf(Gi),|V|/2},where both bounds are sharp.We characterize C satisfying Sdf(C)=1,examine C satisfying Sdf(C)=|V|/2,and determine Sdf(C)when C is a family of vertex-transitive graphs.We also obtain some results on the simultaneous fractional dimension of a graph and its complement.展开更多
基金We thank the National Natural Science Foundation of China(Project No.29975033)the NSF of Guangdong Province(Project No.980340)for financial support.
文摘A new method called spline convolution (SC) for resolving overlapped peaks was proposed in this paper. The differential pulse voltammetric overlapped peaks of mixtures of Pb(II) and Tl(I) were investigated by this method, and satisfactory results were obtained. The results show excellent correlation between peak areas of the processed signals and the concentrations.
文摘If an operator is not invertible, we are interested if there is a subspace such that the reduction of the operator to that subspace is invertible. In this paper we give a spectral approach to generalized inverses considering the subspace determined by the range of the spectral projection associated with an operator and a spectral set containing the point 0. We compare the cases, 0 is a simple pole of the resolvent function, 0 is a pole of order n of the resolvent function, 0 is an isolated point of the spectrum, and 0 is contained in a circularly isolated spectral set.
基金Supported by US-Slovenia Bilateral Collaboration Grant(BI-US/19-21-077)。
文摘For a connected graph G with vertex set V,let RG{x,y}={z∈V:dG(x,z)≠dG(y,z)}for any distinct x,y∈V,where dG(u,w)denotes the length of a shortest uw-path in G.For a real-valued function g defined on V,let g(V)=∑s∈V g(s).Let C={G_(1),G_(2),...,G_(k)}be a family of connected graphs having a common vertex set V,where k≥2 and|V|≥3.A real-valued function h:V→[0,1]is a simultaneous resolving function of C if h(RG{x,y})≥1 for any distinct vertices x,y∈V and for every graph G∈C.The simultaneous fractional dimension,Sdf(C),of C is min{h(V):h is a simultaneous resolving function of C}.In this paper,we initiate the study of the simultaneous fractional dimension of a graph family.We obtain max1≤i≤k{dimf(Gi)}≤Sd_(f)(C)≤min{∑k i=1 dimf(Gi),|V|/2},where both bounds are sharp.We characterize C satisfying Sdf(C)=1,examine C satisfying Sdf(C)=|V|/2,and determine Sdf(C)when C is a family of vertex-transitive graphs.We also obtain some results on the simultaneous fractional dimension of a graph and its complement.
