Segmented all-electron basis set of triple zeta valence quality plus polarization functions(TZP)for the elements of the fifth row to be used together with the zero-order regular approximation(ZORA)is carefully constru...Segmented all-electron basis set of triple zeta valence quality plus polarization functions(TZP)for the elements of the fifth row to be used together with the zero-order regular approximation(ZORA)is carefully constructed.To correctly describe electrons distant from atomic nuclei,the basis set is augmented with diffuse functions giving rise to a set designated as ATZP-ZORA.At the ZORA-B3LYP theoretical level,these sets are used to calculate the ionization energy and mean dipole polarizability of some atoms,bond length,dissociation energy,and harmonic vibrational frequency of diatomic molecules.Then,these results are compared with the theoretical and experimental data found in the literature.Even considering that our sets are relatively compact,they are sufficiently accurate and reliable to perform property calculations involving simultaneously electrons from the inner shell and outer shell.The performances of the ZORA and second-order Douglas-Kroll-Hess Hamiltonians are evaluated and the results are also discussed.展开更多
Abstract. Let D （U, V, W） be an oriented 3-partite graph with ｜ U ｜ = p, ｜V｜ = q and ｜W ｜ = r. For any vertex x in D（U,V,W）, let dx^＋ and dui^- be the outdegree and indegree ofx respectively. Define aui （o...Abstract. Let D （U, V, W） be an oriented 3-partite graph with ｜ U ｜ = p, ｜V｜ = q and ｜W ｜ = r. For any vertex x in D（U,V,W）, let dx^＋ and dui^- be the outdegree and indegree ofx respectively. Define aui （or simply ai） = q ＋ r ＋ dui^＋ - dui^-, bvj （or simply b j） = p ＋ r ＋ d^＋vj - d^-vj and cwk （or simply ck） =p ＋ q ＋ dwk^＋ -dwk^- as the scores of ui in U,vj in V and wk in W respectively. The set A of distinct scores of the vertices of D（U, V, W） is called its score set. In this paper, we prove that if a1 is a non-negative integer, ai（2 ≤ i ≤ n - 1） are even positive integers and an is any positive integer, then for n 〉 3, there exists an oriented 3-partite graph with the score set A ={a1,Σ2i=1 ai,…,Σni=1 ai}, except when A = {0, 2, 3}. Some more results for score sets in oriented 3-partite graphs are obtained.展开更多
A subset of the vertex set of a graph is a feedback vertex set of the graph if the resulting graph is a forest after removed the vertex subset from the graph. A polynomial algorithm for finding a minimum feedback vert...A subset of the vertex set of a graph is a feedback vertex set of the graph if the resulting graph is a forest after removed the vertex subset from the graph. A polynomial algorithm for finding a minimum feedback vertex set of a 3-regular simple graph is provided.展开更多
This paper investigates the fine structure of the Gabor frame generated by the B-spline B<sub>3</sub>. In other words, one extends the known part of the Gabor frame set for the 3-spline with the constructi...This paper investigates the fine structure of the Gabor frame generated by the B-spline B<sub>3</sub>. In other words, one extends the known part of the Gabor frame set for the 3-spline with the construction of the compactly supported dual windows. The frame set of the function B<sub>3</sub> is the subset of all parameters (a,b) ∈R<sup>2</sup>+ </sub>for which the time-frequency shifts of B<sub>3</sub> along aZ × bZ form a Gabor frame for L<sup>2</sup>(R).展开更多
基金the Conselho Nacional de Desenvolvimento Científico Tecnológico(Brazilian Agency)。
文摘Segmented all-electron basis set of triple zeta valence quality plus polarization functions(TZP)for the elements of the fifth row to be used together with the zero-order regular approximation(ZORA)is carefully constructed.To correctly describe electrons distant from atomic nuclei,the basis set is augmented with diffuse functions giving rise to a set designated as ATZP-ZORA.At the ZORA-B3LYP theoretical level,these sets are used to calculate the ionization energy and mean dipole polarizability of some atoms,bond length,dissociation energy,and harmonic vibrational frequency of diatomic molecules.Then,these results are compared with the theoretical and experimental data found in the literature.Even considering that our sets are relatively compact,they are sufficiently accurate and reliable to perform property calculations involving simultaneously electrons from the inner shell and outer shell.The performances of the ZORA and second-order Douglas-Kroll-Hess Hamiltonians are evaluated and the results are also discussed.
文摘Abstract. Let D （U, V, W） be an oriented 3-partite graph with ｜ U ｜ = p, ｜V｜ = q and ｜W ｜ = r. For any vertex x in D（U,V,W）, let dx^＋ and dui^- be the outdegree and indegree ofx respectively. Define aui （or simply ai） = q ＋ r ＋ dui^＋ - dui^-, bvj （or simply b j） = p ＋ r ＋ d^＋vj - d^-vj and cwk （or simply ck） =p ＋ q ＋ dwk^＋ -dwk^- as the scores of ui in U,vj in V and wk in W respectively. The set A of distinct scores of the vertices of D（U, V, W） is called its score set. In this paper, we prove that if a1 is a non-negative integer, ai（2 ≤ i ≤ n - 1） are even positive integers and an is any positive integer, then for n 〉 3, there exists an oriented 3-partite graph with the score set A ={a1,Σ2i=1 ai,…,Σni=1 ai}, except when A = {0, 2, 3}. Some more results for score sets in oriented 3-partite graphs are obtained.
文摘A subset of the vertex set of a graph is a feedback vertex set of the graph if the resulting graph is a forest after removed the vertex subset from the graph. A polynomial algorithm for finding a minimum feedback vertex set of a 3-regular simple graph is provided.
文摘This paper investigates the fine structure of the Gabor frame generated by the B-spline B<sub>3</sub>. In other words, one extends the known part of the Gabor frame set for the 3-spline with the construction of the compactly supported dual windows. The frame set of the function B<sub>3</sub> is the subset of all parameters (a,b) ∈R<sup>2</sup>+ </sub>for which the time-frequency shifts of B<sub>3</sub> along aZ × bZ form a Gabor frame for L<sup>2</sup>(R).
