Two new hereditary classes of P 5-free graphs where the stability number can be found in polynomial time are proposed.They generalize several known results.
We investigate the dominating-c-color number,, of a graph G. That is the maximum number of color classes that are also dominating when G is colored using colors. We show that where is the join of G and . This result a...We investigate the dominating-c-color number,, of a graph G. That is the maximum number of color classes that are also dominating when G is colored using colors. We show that where is the join of G and . This result allows us to construct classes of graphs such that and thus provide some information regarding two questions raised in [1] and [2].展开更多
Let RP（k） denote the k-dimensional real projective space. This article determines which cobordism classes are represented by the total space of a fibering with prescribed base space RP（3）× RP（1）, RP（2） &#...Let RP（k） denote the k-dimensional real projective space. This article determines which cobordism classes are represented by the total space of a fibering with prescribed base space RP（3）× RP（1）, RP（2） × RP（1）, RP（2）× RP（1）× RP（1） or RP（3）× RP（2）.展开更多
In this paper, the author applies adjacent lattice method and Siegel mass formula to determine the classes of positive definite unimodular lattices of rank 4 over Z , and obtains that the class number of unit genus ...In this paper, the author applies adjacent lattice method and Siegel mass formula to determine the classes of positive definite unimodular lattices of rank 4 over Z , and obtains that the class number of unit genus gen( I 4 ) is nine and the class number of even unimodular lattices is three, and also gives the representative lattices of each class.展开更多
In this paper, the author applies adjacent lattice method and Siegel mass formula to determine the classes of positive definite unimodular lattices of rank 4 over Z , and obtains that the class number of unit genus ...In this paper, the author applies adjacent lattice method and Siegel mass formula to determine the classes of positive definite unimodular lattices of rank 4 over Z , and obtains that the class number of unit genus gen( I 4 ) is nine and the class number of even unimodular lattices is three, and also gives the representative lattices of each class.展开更多
Surface wave methods have received much attention due to their efficient, flexible and convenient characteristics. However, there are still critical issues regarding a key step in surface wave inversion. In most exist...Surface wave methods have received much attention due to their efficient, flexible and convenient characteristics. However, there are still critical issues regarding a key step in surface wave inversion. In most existing methods, the number of layers is assumed to be known prior to the process of inversion. However, improper assignment of this parameter leads to erroneous inversion results. A Bayesian nonparametric method for Rayleigh wave inversion is proposed herein to address this problem. In this method, each model class represents a particular number of layers with unknown S-wave velocity and thickness of each layer. As a result, determination of the number of layers is equivalent to selection of the most applicable model class. Regarding each model class, the optimization search of S-wave velocity and thickness of each layer is implemented by using a genetic algorithm. Then, each model class is assessed in view of its efficiency under the Bayesian framework and the most efficient class is selected. Simulated and actual examples verify that the proposed Bayesian nonparametric approach is reliable and efficient for Rayleigh wave inversion, especially for its capability to determine the number of layers.展开更多
基金The first author was supported by DIMACS Summer2 0 0 3Award
文摘Two new hereditary classes of P 5-free graphs where the stability number can be found in polynomial time are proposed.They generalize several known results.
文摘We investigate the dominating-c-color number,, of a graph G. That is the maximum number of color classes that are also dominating when G is colored using colors. We show that where is the join of G and . This result allows us to construct classes of graphs such that and thus provide some information regarding two questions raised in [1] and [2].
基金Project Supported by NSFC (10371029),HNSF (103144)and SRF for ROCS, SEM
文摘Let RP（k） denote the k-dimensional real projective space. This article determines which cobordism classes are represented by the total space of a fibering with prescribed base space RP（3）× RP（1）, RP（2） × RP（1）, RP（2）× RP（1）× RP（1） or RP（3）× RP（2）.
基金Supported by NNSF of China and SF of Chinese Education Committee ,and has been done when the author visited the Department of Mathematics of Purduc Unuversity in 1993
文摘It is a survey of the problem on class numbers of quadratic number fields.
文摘In this paper, the author applies adjacent lattice method and Siegel mass formula to determine the classes of positive definite unimodular lattices of rank 4 over Z , and obtains that the class number of unit genus gen( I 4 ) is nine and the class number of even unimodular lattices is three, and also gives the representative lattices of each class.
文摘In this paper, the author applies adjacent lattice method and Siegel mass formula to determine the classes of positive definite unimodular lattices of rank 4 over Z , and obtains that the class number of unit genus gen( I 4 ) is nine and the class number of even unimodular lattices is three, and also gives the representative lattices of each class.
基金Science and Technology Development Fund of the Macao SAR under research grant SKL-IOTSC-2018-2020the Research Committee of University of Macao under Research Grant MYRG2016-00029-FST。
文摘Surface wave methods have received much attention due to their efficient, flexible and convenient characteristics. However, there are still critical issues regarding a key step in surface wave inversion. In most existing methods, the number of layers is assumed to be known prior to the process of inversion. However, improper assignment of this parameter leads to erroneous inversion results. A Bayesian nonparametric method for Rayleigh wave inversion is proposed herein to address this problem. In this method, each model class represents a particular number of layers with unknown S-wave velocity and thickness of each layer. As a result, determination of the number of layers is equivalent to selection of the most applicable model class. Regarding each model class, the optimization search of S-wave velocity and thickness of each layer is implemented by using a genetic algorithm. Then, each model class is assessed in view of its efficiency under the Bayesian framework and the most efficient class is selected. Simulated and actual examples verify that the proposed Bayesian nonparametric approach is reliable and efficient for Rayleigh wave inversion, especially for its capability to determine the number of layers.
基金supported by the NSFC(1080110530871444)+2 种基金the Key Project of Natural Science of Anhui Provincial Department of Education(KJ2009A44)the Doctoral Special Fund of Hefei University of Technology(GDBJ2010-012)the Key Project of Science and Technology of Anhui Province(08010302070)
文摘In this paper, we give a lower bound exp（2.2 × 10~8 ） for those discriminants of real quadratic fields Q（√ d） with d= N^2-4 and h（d）=1.
