A pathway-based mean-field theory (PBMFT) was recently proposed for E. coli chemotaxis in [G. Si, T. Wu, Q. Quyang and Y. Tu, Phys. Rev. Lett., 109 (2012), 048101]. In this paper, we derived a new moment system of PBMFT by using the moment closure technique in kinetic theory under the assumption that the methylation level is locally concentrated. The new system is hyperbolic with linear convect...

Cyberspace. A consensual hallucination experienced daily by billions of legitimate operators, in every nation, by children being taught mathematical concepts . . . A graphical representation of data abstracted from the banks of every computer in the human system. Unthinkable complexity. Lines of light ranged in the nonspace of the mind, clusters and constellations of data. Like city lights, rec...

Mathematical models and numerical algorithms are explored for several technological challenges in physics, chemistry, aerothermodynamics, and evolution of dynamic systems in economics and weather forecast. Various mathematical concepts are examined to evaluate multifold integrals, dynamics of strange attractors, and solutions of differential equations with small parameters at the highest deriva...

Flexible manufacturing cells (FMCs) often operate with increasing failure rate due to extensive utilization and wear-outs of equipment. While maintenance plans can eliminate wear-out failures, random failures are still unavoidable. This paper discusses a procedure that combines simulation and analytical models to analyze the effects of corrective, preventive, and opportunistic maintenance polic...

Some new ideas in teaching mathematics to engineering students and the implementation of these ideas into the teaching of mechanical engineering students at Brighton University are discussed. The importance of explaining to the students why knowledge of mathematics is essential for their future practical work is emphasized. Mathematics is a language for expressing physical, chemical and enginee...

Vygotsky posed a variety of meaningful ideas for education in his short life. This paper focuses on everyday concepts and mathematical concepts or scientific concepts from his theory, reorganizing these ideas according to a new idea of sublated concepts. Using a series of interviews from a third grade fraction class in Japan, the paper discusses how everyday and mathematical concepts arise out ...

1) The facility with numbers and calculations, 2) The art of avoiding unnecessary calculations, 3) Memorizing formulas and theorems, 4) Understanding and finding proofs, 5) Solving problems with well-described procedures, 6) Solving problems for which there are no well-described procedures, 7) Understanding abstract mathematical concepts, 8) Creating new mathematical concepts, and clarifying an...

This mixed-methods study investigates the effects of student attitudes and behaviours on the outcomes of learning mathematics with computer tools. A computer tool was used to help students develop the mathematical concept of function. In the whole sample (N = 521), student attitudes could account for a 3.4 point difference in test scores between individuals on a 10-point scale. General attitude...