In this paper, we first introduce a new class of generalized accretive operators named （H,η）-accretive in Banach space. By studying the properties of （H,η）-accretive, we extend the concept of resolvent operators...In this paper, we first introduce a new class of generalized accretive operators named （H,η）-accretive in Banach space. By studying the properties of （H,η）-accretive, we extend the concept of resolvent operators associated with m-accretive operators to the new （H,η）-accretive operators. In terms of the new resolvent operator technique, we prove the existence and uniqueness of solutions for this new system of variational inclusions. We also construct a new algorithm for approximating the solution of this system and discuss the convergence of the sequence of iterates generated by the algorithm.展开更多
Let p and q be two distinct primes, epq（n） denotes the largest exponent of power pq which divides n. In this paper, we study the mean value properties of function epq（n）, and give some hybrid mean value formulas f...Let p and q be two distinct primes, epq（n） denotes the largest exponent of power pq which divides n. In this paper, we study the mean value properties of function epq（n）, and give some hybrid mean value formulas for epq（n） and Dirichlet divisor function d（n）. Key words： largest exponent; asymptotic formula; hybrid mean value; Dirichlet divisor function d（n）展开更多
Method development has always been and will continue to be a core driving force of microbiome science, In this perspective, we argue that in the next decade, method development in microbiome analysis will be driven by...Method development has always been and will continue to be a core driving force of microbiome science, In this perspective, we argue that in the next decade, method development in microbiome analysis will be driven by three key changes in both ways of thinking and technological platforms： ① a shift from dissecting microbiota structure by sequencing to tracking microbiota state, function, and intercellular interaction via imaging; ② a shift from interrogating a consortium or population of cells to probing individual cells; and ③a shift from microbiome data analysis to microbiome data science. Some of the recent methoddevelopment efforts by Chinese microbiome scientists and their international collaborators that underlie these technological trends are highlighted here. It is our belief that the China Microbiome Initiative has the opportunity to deliver outstanding ＂Made-in-China＂ tools to the international research community, by building an ambitious, competitive, and collaborative program at the forefront of method development for microbiome science.展开更多
This study compares the subject matter appeared on traditional Thai textbooks and Japanese textbooks and analyzes how extension and integration sequence on Japanese textbooks evokes students＇ mathematical creativity....This study compares the subject matter appeared on traditional Thai textbooks and Japanese textbooks and analyzes how extension and integration sequence on Japanese textbooks evokes students＇ mathematical creativity. The data were collected from the series of four lessons in the fifth grade by teaching experiment methodology conducted following the professional development project implemented lesson study and open approach in Thailand. The results show that extension and integration sequence is an appropriate subject matter to generate lesson for problem-solving classroom. The sequence of lesson leads students to excitement, curiosity, confidence and intimacy in mathematics that are powerful effects of mathematical creativity. Students can produce the different and various ways to solve problems that indicate their divergent thinking.展开更多
文摘In this paper, we first introduce a new class of generalized accretive operators named （H,η）-accretive in Banach space. By studying the properties of （H,η）-accretive, we extend the concept of resolvent operators associated with m-accretive operators to the new （H,η）-accretive operators. In terms of the new resolvent operator technique, we prove the existence and uniqueness of solutions for this new system of variational inclusions. We also construct a new algorithm for approximating the solution of this system and discuss the convergence of the sequence of iterates generated by the algorithm.
文摘Let p and q be two distinct primes, epq（n） denotes the largest exponent of power pq which divides n. In this paper, we study the mean value properties of function epq（n）, and give some hybrid mean value formulas for epq（n） and Dirichlet divisor function d（n）. Key words： largest exponent; asymptotic formula; hybrid mean value; Dirichlet divisor function d（n）
基金We are grateful to the support from the National Natural Science Foundation of China （NSFC） （31425002, 91231205, 81430011, 61303161, 31470220, and 31327001）, and the Frontier Science Research Program, the Soil-Microbe System Function and Regulation Program, and the Science and Technology Service Network Initiative （STS） from the Chinese Academy of Sciences （CAS）.
文摘Method development has always been and will continue to be a core driving force of microbiome science, In this perspective, we argue that in the next decade, method development in microbiome analysis will be driven by three key changes in both ways of thinking and technological platforms： ① a shift from dissecting microbiota structure by sequencing to tracking microbiota state, function, and intercellular interaction via imaging; ② a shift from interrogating a consortium or population of cells to probing individual cells; and ③a shift from microbiome data analysis to microbiome data science. Some of the recent methoddevelopment efforts by Chinese microbiome scientists and their international collaborators that underlie these technological trends are highlighted here. It is our belief that the China Microbiome Initiative has the opportunity to deliver outstanding ＂Made-in-China＂ tools to the international research community, by building an ambitious, competitive, and collaborative program at the forefront of method development for microbiome science.
文摘This study compares the subject matter appeared on traditional Thai textbooks and Japanese textbooks and analyzes how extension and integration sequence on Japanese textbooks evokes students＇ mathematical creativity. The data were collected from the series of four lessons in the fifth grade by teaching experiment methodology conducted following the professional development project implemented lesson study and open approach in Thailand. The results show that extension and integration sequence is an appropriate subject matter to generate lesson for problem-solving classroom. The sequence of lesson leads students to excitement, curiosity, confidence and intimacy in mathematics that are powerful effects of mathematical creativity. Students can produce the different and various ways to solve problems that indicate their divergent thinking.
