Partition of unity based numerical manifold method can solve continuous and discontinuous problems in a unified framework with a two-cover system,i.e.,the mathematical cover and physical cover.However,renewal of the t...Partition of unity based numerical manifold method can solve continuous and discontinuous problems in a unified framework with a two-cover system,i.e.,the mathematical cover and physical cover.However,renewal of the topology of the two-cover system poses a challenge for multiple crack propagation problems and there are few references.In this study,a robust and efficient strategy is proposed to update the cover system of the numerical manifold method in simulation of multiple crack propagation problems.The proposed algorithm updates the cover system with a bottom-up process:1)identification of fractured manifold elements according to the previous and latest crack tip position;and 2)local topological update of the manifold elements,physical patches,block boundary loops,and non-persistent joint loops according to the scenario classification of the propagating crack.The proposed crack tracking strategy and classification of the renewal cases promote a robust and efficient cover renewal algorithm for multiple crack propagation analysis.Three crack propagation examples show that the proposed algorithm performs well in updating the cover system.This cover renewal methodology can be extended for numerical manifold method with polygonal mathematical covers.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
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
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
A fuzzy integral based way of measurement assessment has been established by using linguistic varia-bles and combining fuzzy integral with hierarchy analysis for measurement of medium and small enterprises'product...A fuzzy integral based way of measurement assessment has been established by using linguistic varia-bles and combining fuzzy integral with hierarchy analysis for measurement of medium and small enterprises'product innovation. The conclusions drawn from analyses made with 20 medium and small enterprises providebases for governments to formulate applicable policies and for medium and small enterprises to enhance theirproduct innovation.展开更多
Mathematics is one of the basic courses of public university freshmen non-math majors, it is an important tool for students to learn the successor program, and the learning process can develop and exercise their think...Mathematics is one of the basic courses of public university freshmen non-math majors, it is an important tool for students to learn the successor program, and the learning process can develop and exercise their thinking and ability. Given the differences in different periods of higher mathematics learning objects, as well as students learning content in different periods and in different conditions, teachers in the teaching mode of teaching could be considered stage of teaching. That is, different content based on various stages of teaching and student learning, and use different teaching methods and means to carry out teaching.展开更多
基金Project(51321065,51479191,11672360)supported by the National Natural Science Foundation of China。
文摘Partition of unity based numerical manifold method can solve continuous and discontinuous problems in a unified framework with a two-cover system,i.e.,the mathematical cover and physical cover.However,renewal of the topology of the two-cover system poses a challenge for multiple crack propagation problems and there are few references.In this study,a robust and efficient strategy is proposed to update the cover system of the numerical manifold method in simulation of multiple crack propagation problems.The proposed algorithm updates the cover system with a bottom-up process:1)identification of fractured manifold elements according to the previous and latest crack tip position;and 2)local topological update of the manifold elements,physical patches,block boundary loops,and non-persistent joint loops according to the scenario classification of the propagating crack.The proposed crack tracking strategy and classification of the renewal cases promote a robust and efficient cover renewal algorithm for multiple crack propagation analysis.Three crack propagation examples show that the proposed algorithm performs well in updating the cover system.This cover renewal methodology can be extended for numerical manifold method with polygonal mathematical covers.
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.
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）
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.
基金Sponsored by the National Natural Science Foundation of China (Grant No. 70171039)Major Project of the National Natural Science Foundation of China (Grant No. 70131010 )Natural Science Foundation of Heilongjiang Province (Grant No. G01-09)
文摘A fuzzy integral based way of measurement assessment has been established by using linguistic varia-bles and combining fuzzy integral with hierarchy analysis for measurement of medium and small enterprises'product innovation. The conclusions drawn from analyses made with 20 medium and small enterprises providebases for governments to formulate applicable policies and for medium and small enterprises to enhance theirproduct innovation.
文摘Mathematics is one of the basic courses of public university freshmen non-math majors, it is an important tool for students to learn the successor program, and the learning process can develop and exercise their thinking and ability. Given the differences in different periods of higher mathematics learning objects, as well as students learning content in different periods and in different conditions, teachers in the teaching mode of teaching could be considered stage of teaching. That is, different content based on various stages of teaching and student learning, and use different teaching methods and means to carry out teaching.
