This paper presents a mathematical model for components/parts unification (CPU) policy. This model considers two components/parts that are functionally interchangeable but purchased from suppliers with different price...This paper presents a mathematical model for components/parts unification (CPU) policy. This model considers two components/parts that are functionally interchangeable but purchased from suppliers with different prices and quality characteristics. Because of the buyer's quality preference and suppliers' discount rates for bulky purchases, the model assists the procurement manager to determine how best to purchase the components/parts to meet its demand while minimizing the total acquisition costs.展开更多
The more unambiguous statement of the P versus NP problem and the judgement of its hardness, are the key ways to find the full proof of the P versus NP problem. There are two sub-problems in the P versus NP problem. T...The more unambiguous statement of the P versus NP problem and the judgement of its hardness, are the key ways to find the full proof of the P versus NP problem. There are two sub-problems in the P versus NP problem. The first is the classifications of different mathematical problems (languages), and the second is the distinction between a non-deterministic Turing machine (NTM) and a deterministic Turing machine (DTM). The process of an NTM can be a power set of the corresponding DTM, which proves that the states of an NTM can be a power set of the corresponding DTM. If combining this viewpoint with Cantor's theorem, it is shown that an NTM is not equipotent to a DTM. This means that "generating the power set P(A) of a set A" is a non-canonical example to support that P is not equal to NP.展开更多
Using the method of matched asymptotic expansions, the shock solutions for a class of singularly perturbed nonlinear problems are discussed. The relation of the shock solutions and their boundary conditions is obtaine...Using the method of matched asymptotic expansions, the shock solutions for a class of singularly perturbed nonlinear problems are discussed. The relation of the shock solutions and their boundary conditions is obtained. And the known results are generalized.展开更多
According to the actual engineering problem that the precise load model of shield machine is difficult to achieve,a design method of sliding mode robust controller oriented to the automatic rectification of shield mac...According to the actual engineering problem that the precise load model of shield machine is difficult to achieve,a design method of sliding mode robust controller oriented to the automatic rectification of shield machine was proposed. Firstly,the nominal load model of shield machine and the ranges of model parameters were obtained by the soil mechanics parameters of certain geological conditions and the messages of the self-learning of shield machine by tunneling for previous segments. Based on this rectification mechanism model with known ranges of parameters,a sliding mode robust controller was proposed. Finally,the simulation analysis was developed to verify the effectiveness of the proposed controller. The simulation results show that the sliding mode robust controller can be implemented in the attitude rectification process of the shield machine and it has stronger robustness to overcome the soil disturbance.展开更多
When solving a mathematical problem, we sometimes encounter a situation where we can not reach a correct answer in spite of acquiring knowledge and formula necessary for the solution. The reason can be attributed to t...When solving a mathematical problem, we sometimes encounter a situation where we can not reach a correct answer in spite of acquiring knowledge and formula necessary for the solution. The reason can be attributed to the lack in metacognitive abilities. Metacognitive abilities consist of comparing the difficulty of problem with own ability, proper plan of solution process, and conscious monitoring and control of solution process. The role and importance of metacognitive ability in mathematical problem solving of permutations and combinations was explored. Participants were required to solve five practical problems related to permutations and combinations. For each problem, the solution process was divided into： （1） understanding （recognition） of mathematical problem; （2） plan of solution; （3） execution of solution. Participants were also required to rate the anticipation whether they could solve it or not, and to rate the confidence of their own answer. According to the total score of five problems, the participants were categorized into the group of the high test score and the group of the low test score. As a result, at the plan and the execution processes, statistically significant differences were detected between the high and the low score groups. As for the rating on the anticipation of result and the confidence of own answer, no significant differences were found between both groups. Moreover, the relationship between the score of plan process and the score of execution process was statistically correlated. In other words, the more proper the plan process was conducted, the more proper solution the participants reached. In such a way, the importance of metacognitive ability in the solving process, especially the plan ability, was suggested.展开更多
We investigated the use of diagrams in multiplicative comparison word problems. The diagrams have been considered as one of the effective heuristic strategies or solving math problems. However, how students use during...We investigated the use of diagrams in multiplicative comparison word problems. The diagrams have been considered as one of the effective heuristic strategies or solving math problems. However, how students use during their school and the degree development that shows in their performance when applied to specific fields of knowledge is a task to be elucidated. We place our study in the school stage in which it makes the transition from arithmetic to algebra and arithmetic problems we focus on in the underlying multiplicative comparison scheme. In this paper, we analyzed the responses of high school students to the translation of multiplicative comparison word problems to representation graphs. We have used the responses of 12 -14 year old students （freshman year of secondary school） to represent multiplicative comparison word problems to identify and categorize the students responses, which allowed us identify categories for each type of representation and hypothesize priority order and subordination between the categories. Results show that students are not familiar with building diagrams that integrate existing relations in word problems. Most of the students do not use all the quantitative information contained in the word problem, therefore draw diagrams referring to the subject or context of the problem without relating to the data in it. We describe in detail the quantitative diagram types produced by these students. We have identified four kinds of quantitative diagrams that the students used to represent the multiplicative comparison problems with inconsistent statements, and these diagrams correspond to the four strategies for tackling the construction of the diagram.展开更多
文摘This paper presents a mathematical model for components/parts unification (CPU) policy. This model considers two components/parts that are functionally interchangeable but purchased from suppliers with different prices and quality characteristics. Because of the buyer's quality preference and suppliers' discount rates for bulky purchases, the model assists the procurement manager to determine how best to purchase the components/parts to meet its demand while minimizing the total acquisition costs.
文摘The more unambiguous statement of the P versus NP problem and the judgement of its hardness, are the key ways to find the full proof of the P versus NP problem. There are two sub-problems in the P versus NP problem. The first is the classifications of different mathematical problems (languages), and the second is the distinction between a non-deterministic Turing machine (NTM) and a deterministic Turing machine (DTM). The process of an NTM can be a power set of the corresponding DTM, which proves that the states of an NTM can be a power set of the corresponding DTM. If combining this viewpoint with Cantor's theorem, it is shown that an NTM is not equipotent to a DTM. This means that "generating the power set P(A) of a set A" is a non-canonical example to support that P is not equal to NP.
基金Supported by the National Natural Science Foundation of China（10471039） Supported by the E-Institutes of Shanghai Municipal Education Commission（E03004） Supported by the Natural Science Foundation of Zhejiang Province（Y606268）
文摘Using the method of matched asymptotic expansions, the shock solutions for a class of singularly perturbed nonlinear problems are discussed. The relation of the shock solutions and their boundary conditions is obtained. And the known results are generalized.
基金Project(2007CB714006) supported by the National Basic Research Program of China
文摘According to the actual engineering problem that the precise load model of shield machine is difficult to achieve,a design method of sliding mode robust controller oriented to the automatic rectification of shield machine was proposed. Firstly,the nominal load model of shield machine and the ranges of model parameters were obtained by the soil mechanics parameters of certain geological conditions and the messages of the self-learning of shield machine by tunneling for previous segments. Based on this rectification mechanism model with known ranges of parameters,a sliding mode robust controller was proposed. Finally,the simulation analysis was developed to verify the effectiveness of the proposed controller. The simulation results show that the sliding mode robust controller can be implemented in the attitude rectification process of the shield machine and it has stronger robustness to overcome the soil disturbance.
文摘When solving a mathematical problem, we sometimes encounter a situation where we can not reach a correct answer in spite of acquiring knowledge and formula necessary for the solution. The reason can be attributed to the lack in metacognitive abilities. Metacognitive abilities consist of comparing the difficulty of problem with own ability, proper plan of solution process, and conscious monitoring and control of solution process. The role and importance of metacognitive ability in mathematical problem solving of permutations and combinations was explored. Participants were required to solve five practical problems related to permutations and combinations. For each problem, the solution process was divided into： （1） understanding （recognition） of mathematical problem; （2） plan of solution; （3） execution of solution. Participants were also required to rate the anticipation whether they could solve it or not, and to rate the confidence of their own answer. According to the total score of five problems, the participants were categorized into the group of the high test score and the group of the low test score. As a result, at the plan and the execution processes, statistically significant differences were detected between the high and the low score groups. As for the rating on the anticipation of result and the confidence of own answer, no significant differences were found between both groups. Moreover, the relationship between the score of plan process and the score of execution process was statistically correlated. In other words, the more proper the plan process was conducted, the more proper solution the participants reached. In such a way, the importance of metacognitive ability in the solving process, especially the plan ability, was suggested.
文摘We investigated the use of diagrams in multiplicative comparison word problems. The diagrams have been considered as one of the effective heuristic strategies or solving math problems. However, how students use during their school and the degree development that shows in their performance when applied to specific fields of knowledge is a task to be elucidated. We place our study in the school stage in which it makes the transition from arithmetic to algebra and arithmetic problems we focus on in the underlying multiplicative comparison scheme. In this paper, we analyzed the responses of high school students to the translation of multiplicative comparison word problems to representation graphs. We have used the responses of 12 -14 year old students （freshman year of secondary school） to represent multiplicative comparison word problems to identify and categorize the students responses, which allowed us identify categories for each type of representation and hypothesize priority order and subordination between the categories. Results show that students are not familiar with building diagrams that integrate existing relations in word problems. Most of the students do not use all the quantitative information contained in the word problem, therefore draw diagrams referring to the subject or context of the problem without relating to the data in it. We describe in detail the quantitative diagram types produced by these students. We have identified four kinds of quantitative diagrams that the students used to represent the multiplicative comparison problems with inconsistent statements, and these diagrams correspond to the four strategies for tackling the construction of the diagram.
