Given a graph G and a positive integer d, an L( d, 1) -labeling of G is afunction / that assigns to each vertex of G a non-negative integer such that |f(u)-f (v) | >=d ifd_c(u, v) =1;|f(u)-f(v) | >=1 if d_c(u, v...Given a graph G and a positive integer d, an L( d, 1) -labeling of G is afunction / that assigns to each vertex of G a non-negative integer such that |f(u)-f (v) | >=d ifd_c(u, v) =1;|f(u)-f(v) | >=1 if d_c(u, v) =2. The L(d, 1)-labeling number of G, lambda_d(G) is theminimum range span of labels over all such labelings, which is motivated by the channel assignmentproblem. We consider the question of finding the minimum edge span beta_d( G) of this labeling.Several classes of graphs such as cycles, trees, complete k-partite graphs, chordal graphs includingtriangular lattice and square lattice which are important to a telecommunication problem arestudied, and exact values are given.展开更多
L(d, 1)-labeling is a kind of graph coloring problem from frequency assignment in radio networks, in which adjacent nodes must receive colors that are at least d apart while nodes at distance two from each other must ...L(d, 1)-labeling is a kind of graph coloring problem from frequency assignment in radio networks, in which adjacent nodes must receive colors that are at least d apart while nodes at distance two from each other must receive different colors. We focus on L(d, 1)-labeling of regular tilings for d≥3 since the cases d=0, 1 or 2 have been researched by Calamoneri and Petreschi. For all three kinds of regular tilings, we give their L (d, 1)-labeling numbers for any integer d≥3. Therefore, combined with the results given by Calamoneri and Petreschi, the L(d, 1)-labeling numbers of regular tilings for any nonnegative integer d may be determined completely.展开更多
A k-L(2,1)-labeling for a graph G is a function such that whenever and whenever u and v are at distance two apart. The λ-number for G, denoted by λ(G), is the minimum k over all k-L(2,1)-labelings of G. In this pape...A k-L(2,1)-labeling for a graph G is a function such that whenever and whenever u and v are at distance two apart. The λ-number for G, denoted by λ(G), is the minimum k over all k-L(2,1)-labelings of G. In this paper, we show that for or 11, which confirms Conjecture 6.1 stated in [X. Li, V. Mak-Hau, S. Zhou, The L(2,1)-labelling problem for cubic Cayley graphs on dihedral groups, J. Comb. Optim. (2013) 25: 716-736] in the case when or 11. Moreover, we show that? if 1) either (mod 6), m is odd, r = 3, or 2) (mod 3), m is even (mod 2), r = 0.展开更多
In this paper, we built upon the estimating primaries by sparse inversion （EPSI） method. We use the 3D curvelet transform and modify the EPSI method to the sparse inversion of the biconvex optimization and Ll-norm r...In this paper, we built upon the estimating primaries by sparse inversion （EPSI） method. We use the 3D curvelet transform and modify the EPSI method to the sparse inversion of the biconvex optimization and Ll-norm regularization, and use alternating optimization to directly estimate the primary reflection coefficients and source wavelet. The 3D curvelet transform is used as a sparseness constraint when inverting the primary reflection coefficients, which results in avoiding the prediction subtraction process in the surface-related multiples elimination （SRME） method. The proposed method not only reduces the damage to the effective waves but also improves the elimination of multiples. It is also a wave equation- based method for elimination of surface multiple reflections, which effectively removes surface multiples under complex submarine conditions.展开更多
首次采用反相高效液相色谱法测定茜草根中1,3,6-trihydroxy-2-methylanthraquinone-3-O-[3-O-acetyl-α-L-rhamnopyranosyl-(1→2)-β-D-glucopyranoside]的含量。色谱柱为Purospher star RP C18色谱柱(250mm×4.6mm,5μm),流动相...首次采用反相高效液相色谱法测定茜草根中1,3,6-trihydroxy-2-methylanthraquinone-3-O-[3-O-acetyl-α-L-rhamnopyranosyl-(1→2)-β-D-glucopyranoside]的含量。色谱柱为Purospher star RP C18色谱柱(250mm×4.6mm,5μm),流动相为甲醇:水:四氢呋喃(65:34.7:0.3),流速为1.0mL/min,检测波长为276nm,柱温为25℃。该方法的线性范围为0.020~0.160μg,r=0.9998,平均回收率为101.5%,RSD为2.0%(n=6)。该方法测定1,3,6-trihydroxy-2-methylanthraquinone-3-O-[3-O-acetyl-α-L-rhamnopyranosyl-(1→2)-β-D-glucopyranoside]含量灵敏、准确、重现性好。展开更多
文摘Given a graph G and a positive integer d, an L( d, 1) -labeling of G is afunction / that assigns to each vertex of G a non-negative integer such that |f(u)-f (v) | >=d ifd_c(u, v) =1;|f(u)-f(v) | >=1 if d_c(u, v) =2. The L(d, 1)-labeling number of G, lambda_d(G) is theminimum range span of labels over all such labelings, which is motivated by the channel assignmentproblem. We consider the question of finding the minimum edge span beta_d( G) of this labeling.Several classes of graphs such as cycles, trees, complete k-partite graphs, chordal graphs includingtriangular lattice and square lattice which are important to a telecommunication problem arestudied, and exact values are given.
文摘L(d, 1)-labeling is a kind of graph coloring problem from frequency assignment in radio networks, in which adjacent nodes must receive colors that are at least d apart while nodes at distance two from each other must receive different colors. We focus on L(d, 1)-labeling of regular tilings for d≥3 since the cases d=0, 1 or 2 have been researched by Calamoneri and Petreschi. For all three kinds of regular tilings, we give their L (d, 1)-labeling numbers for any integer d≥3. Therefore, combined with the results given by Calamoneri and Petreschi, the L(d, 1)-labeling numbers of regular tilings for any nonnegative integer d may be determined completely.
文摘A k-L(2,1)-labeling for a graph G is a function such that whenever and whenever u and v are at distance two apart. The λ-number for G, denoted by λ(G), is the minimum k over all k-L(2,1)-labelings of G. In this paper, we show that for or 11, which confirms Conjecture 6.1 stated in [X. Li, V. Mak-Hau, S. Zhou, The L(2,1)-labelling problem for cubic Cayley graphs on dihedral groups, J. Comb. Optim. (2013) 25: 716-736] in the case when or 11. Moreover, we show that? if 1) either (mod 6), m is odd, r = 3, or 2) (mod 3), m is even (mod 2), r = 0.
基金supported by the National Science and Technology Major Project (No.2011ZX05023-005-008)
文摘In this paper, we built upon the estimating primaries by sparse inversion （EPSI） method. We use the 3D curvelet transform and modify the EPSI method to the sparse inversion of the biconvex optimization and Ll-norm regularization, and use alternating optimization to directly estimate the primary reflection coefficients and source wavelet. The 3D curvelet transform is used as a sparseness constraint when inverting the primary reflection coefficients, which results in avoiding the prediction subtraction process in the surface-related multiples elimination （SRME） method. The proposed method not only reduces the damage to the effective waves but also improves the elimination of multiples. It is also a wave equation- based method for elimination of surface multiple reflections, which effectively removes surface multiples under complex submarine conditions.
文摘首次采用反相高效液相色谱法测定茜草根中1,3,6-trihydroxy-2-methylanthraquinone-3-O-[3-O-acetyl-α-L-rhamnopyranosyl-(1→2)-β-D-glucopyranoside]的含量。色谱柱为Purospher star RP C18色谱柱(250mm×4.6mm,5μm),流动相为甲醇:水:四氢呋喃(65:34.7:0.3),流速为1.0mL/min,检测波长为276nm,柱温为25℃。该方法的线性范围为0.020~0.160μg,r=0.9998,平均回收率为101.5%,RSD为2.0%(n=6)。该方法测定1,3,6-trihydroxy-2-methylanthraquinone-3-O-[3-O-acetyl-α-L-rhamnopyranosyl-(1→2)-β-D-glucopyranoside]含量灵敏、准确、重现性好。
