The total chromatic number xT（G） of a graph G is the minimum number of colors needed to color the elements（vertices and edges） of G such that no adjacent or incident pair of elements receive the same color, G is c...The total chromatic number xT（G） of a graph G is the minimum number of colors needed to color the elements（vertices and edges） of G such that no adjacent or incident pair of elements receive the same color, G is called Type 1 if xT（G） =△（G）＋1. In this paper we prove that the join of a complete bipartite graph Km,n and a cycle Cn is of Type 1.展开更多
The purpose of the study was to use the Problem-Centered Double-Cycles Instructional Model （PCDC-IM） （1995, Chang） to help the teacher （Lin） implement model-eliciting activity （MEA） in her mathematics classes....The purpose of the study was to use the Problem-Centered Double-Cycles Instructional Model （PCDC-IM） （1995, Chang） to help the teacher （Lin） implement model-eliciting activity （MEA） in her mathematics classes. In this study, there were 31 students divided in 10 groups and engaged in the MEA ＂Who saved the oriental cherry trees＂. Data collections included the learning sheets, journals and debriefing forms of students, teaching and reflection journals, observation reports, and field notes of teachers, reflection journals and interview reports of researchers, video tapes and records of the classes and meetings. There were four parts of the teaching cycle in PCDC-IM, namely task, guidance, environment and analysis. We summarized developing and implementing the MEA in ＂Task＂ aspect, 5 principles and 5 kinds of teachers＇ roles in ＂Guidance＂ aspect, 2 elements and 5 features in ＂Environment＂ aspect and data in ＂Analysis＂ aspect. The findings showed that PCDC-IM was helpful for mathematics teachers who want to change their instruction from lecture into modeling teaching.展开更多
In this paper, we will study the adjacent strong edge coloring of series-parallel graphs, and prove that series-parallel graphs of △(G) = 3 and 4 satisfy the conjecture of adjacent strong edge coloring using the doub...In this paper, we will study the adjacent strong edge coloring of series-parallel graphs, and prove that series-parallel graphs of △(G) = 3 and 4 satisfy the conjecture of adjacent strong edge coloring using the double inductions and the method of exchanging colors from the aspect of configuration property. For series-parallel graphs of △(G) ≥ 5, △(G) ≤ x'as(G) ≤ △(G) + 1. Moreover, x'as(G) = △(G) + 1 if and only if it has two adjacent vertices of maximum degree, where △(G) and X'as(G) denote the maximum degree and the adjacent strong edge chromatic number of graph G respectively.展开更多
Meiosis is pivotal for sexual reproduction and fertility. Meiotic programmed DNA double-strand breaks(DSBs) initiate homologous recombination, ensuring faithful chromosome segregation and generation of gametes. Howeve...Meiosis is pivotal for sexual reproduction and fertility. Meiotic programmed DNA double-strand breaks(DSBs) initiate homologous recombination, ensuring faithful chromosome segregation and generation of gametes. However, few studies have focused on meiotic DSB formation in human reproduction.Here, we report four infertile siblings born to a consanguineous marriage, with three brothers suffering from non-obstructive azoospermia and one sister suffering from unexplained infertility with normal menstrual cycles and normal ovary sizes with follicular activity. An autosomal recessive mutation in TOP6BL was found co-segregating with infertility in this family. Investigation of one male patient revealed failure in programmed meiotic DSB formation and meiotic arrest prior to pachytene stage of prophase I.Mouse models carrying similar mutations to that in patients recapitulated the spermatogenic abnormalities of the patient. Pathogenicity of the mutation in the female patient was supported by observations in mice that meiotic programmed DSBs failed to form in mutant oocytes and oocyte maturation failure due to absence of meiotic recombination. Our study thus illustrates the phenotypical characteristics and the genotype-phenotype correlations of meiotic DSB formation failure in humans.展开更多
文摘The total chromatic number xT（G） of a graph G is the minimum number of colors needed to color the elements（vertices and edges） of G such that no adjacent or incident pair of elements receive the same color, G is called Type 1 if xT（G） =△（G）＋1. In this paper we prove that the join of a complete bipartite graph Km,n and a cycle Cn is of Type 1.
文摘The purpose of the study was to use the Problem-Centered Double-Cycles Instructional Model （PCDC-IM） （1995, Chang） to help the teacher （Lin） implement model-eliciting activity （MEA） in her mathematics classes. In this study, there were 31 students divided in 10 groups and engaged in the MEA ＂Who saved the oriental cherry trees＂. Data collections included the learning sheets, journals and debriefing forms of students, teaching and reflection journals, observation reports, and field notes of teachers, reflection journals and interview reports of researchers, video tapes and records of the classes and meetings. There were four parts of the teaching cycle in PCDC-IM, namely task, guidance, environment and analysis. We summarized developing and implementing the MEA in ＂Task＂ aspect, 5 principles and 5 kinds of teachers＇ roles in ＂Guidance＂ aspect, 2 elements and 5 features in ＂Environment＂ aspect and data in ＂Analysis＂ aspect. The findings showed that PCDC-IM was helpful for mathematics teachers who want to change their instruction from lecture into modeling teaching.
基金National Natural Science Foundation of China (60103021, 60274026)
文摘In this paper, we will study the adjacent strong edge coloring of series-parallel graphs, and prove that series-parallel graphs of △(G) = 3 and 4 satisfy the conjecture of adjacent strong edge coloring using the double inductions and the method of exchanging colors from the aspect of configuration property. For series-parallel graphs of △(G) ≥ 5, △(G) ≤ x'as(G) ≤ △(G) + 1. Moreover, x'as(G) = △(G) + 1 if and only if it has two adjacent vertices of maximum degree, where △(G) and X'as(G) denote the maximum degree and the adjacent strong edge chromatic number of graph G respectively.
基金supported by the National Key Research and Developmental Program of China (2018YFC1003700, 2016YFC1000600, 2018YFC1003400 and 2018YFC1004700)the Strategic Priority Research Program of the Chinese Academy of Sciences (XDB19000000)the National Natural Science Foundation of China (31890780, 31630050, 31871514 and 31771668)。
文摘Meiosis is pivotal for sexual reproduction and fertility. Meiotic programmed DNA double-strand breaks(DSBs) initiate homologous recombination, ensuring faithful chromosome segregation and generation of gametes. However, few studies have focused on meiotic DSB formation in human reproduction.Here, we report four infertile siblings born to a consanguineous marriage, with three brothers suffering from non-obstructive azoospermia and one sister suffering from unexplained infertility with normal menstrual cycles and normal ovary sizes with follicular activity. An autosomal recessive mutation in TOP6BL was found co-segregating with infertility in this family. Investigation of one male patient revealed failure in programmed meiotic DSB formation and meiotic arrest prior to pachytene stage of prophase I.Mouse models carrying similar mutations to that in patients recapitulated the spermatogenic abnormalities of the patient. Pathogenicity of the mutation in the female patient was supported by observations in mice that meiotic programmed DSBs failed to form in mutant oocytes and oocyte maturation failure due to absence of meiotic recombination. Our study thus illustrates the phenotypical characteristics and the genotype-phenotype correlations of meiotic DSB formation failure in humans.
