Every Continuous Operator Has an Invariant Measure

We prove the existence of an invariant measure for a large class of random processes with discrete time without assuming their linearity. Our main examples are “processes with variable length”, in which components may appear and disappear in the course of functioning. One of these examples displays non-uniqueness of invariant measure in a 1-D process.     

Extending the GGobi pipeline from R

This paper describes progress towards developing a platform for rapid prototyping of interactive data visualizations, using R, GGobi, rggobi and RGtk2. GGobi is a software tool for multivariate interactive graphics. At the core of GGobi is a data pipeline that incrementally transforms data through a series of stages into a plot and maps user interaction with the plot back to the data. The GGobi pipeline is extensible and mutable at runtime. The rggobi package, an interface from the R language to GGobi, has been augmented with a low-level interface that supports the customization of interactive data visualizations through the extension and manipulation of the GGobi pipeline. The large size of the GGobi API has motivated the use of the RGtk2 code generation system to create the low-level interface between R and GGobi. The software is demonstrated through an application to interactive network visualization.     

电磁学教学必须重视演示实验

阐述了电磁学演示实验的重要性及提高高校电磁学演示实验水平的途径.     

运用多媒体技术优化物理演示实验教学

利用多媒体计算机结合摄像头、麦克风等配置对物理演示实验进行优化,解决了部分演示实验中存在的能见度低、直观性不强等缺点,大大提高了相关演示实验的水平,取得了较好的教学效果.     

Robust optimization for interactive multiobjective programming with imprecise information applied to R&D project portfolio selection

A multiobjective binary integer programming model for R&D project portfolio selection with competing objectives is developed when problem coefficients in both objective functions and constraints are uncertain. Robust optimization is used in dealing with uncertainty while an interactive procedure is used in making tradeoffs among the multiple objectives. Robust nondominated solutions are generated by solving the linearized counterpart of the robust augmented weighted Tchebycheff programs. A decision maker’s most preferred solution is identified in the interactive robust weighted Tchebycheff procedure by progressively eliciting and incorporating the decision maker’s preference information into the solution process. An example is presented to illustrate the solution approach and performance. The developed approach can also be applied to general multiobjective mixed integer programming problems.     

Using interactive algebra software to support a discourse community

In this work we studied the impact of using NuCalc, an interactive computer algebra software, on the development of a discourse community in a college level mathematics class. Qualitative and quantitative data were collected over the course of 3 weeks of instruction. We examined the influence of the software on: group interactions; the mathematical investigations of learners; and the teacher’s interactions with students. Data points to four distinct ways in which the presence of NuCalc positively impacted the learning community we studied: (1) it served as a tool for extending students’ mathematical thinking, (2) it motivated students’ engagement in group discourse, (3) it became a tool for mediating discourse, (4) it became a catalyst for refining the culture of classroom, shifting the patterns of interactions between the teacher and learners.     

互联网+《高聚物合成工艺学》教学研究与实践

掌握高聚物合成工艺的过程与控制是高分子工程类专业学生必须具备的最基本技能。本校《高聚物合成工艺学》的课程教学以直观化、互动教学为基础,探索教学模式的革新,以培养学生的独立思考、工程实践能力并提高教学质量。随着"互联网+教学"的发展,微课、翻转课堂、慕课等教学形式给教师提供了很多可借鉴的手段,师生在课程教学活动中作用实现反转。基于原有教学方法及考核模式的研究,本文以《高聚物合成工艺学》的教学革新为目标,探索互联网+《高聚物合成工艺学》教学改革的一些教学思维和实践,仅供同行教师优化课程教学方法、提高教学质量参考。     

New approaches in computational dynamics of the mixing flow

Between the most mature interdisciplinary areas, computational fluid dynamics (CFD) comes recently into focus. In the same time, it becomes more and more difficult to contribute fundamental research to it. However, although it remains unpredictable how CFD develops, it is part of what makes it an exciting and attractive discipline.This paper aims to exhibit some part of recent work in CFD. It concerns the qualitative approach of the turbulent behaviour of a mixing flow in an excitable media. Studying a mixing for a flow implies the analysis of successive stretching and folding phenomena for its particles, the influence of parameters and initial conditions. In the previous works, the study of the 3D non-periodic models exhibited a quite complicated behaviour. In agreement with experiments, there were involved some significant events, the so-called “rare events”. The variation of parameters had a great influence on the length and surface deformations. The experiments were realized with a special vortex installation, it was used a well-known aquatic algae as biologic material, and the water as basic fluid.In the paper there are presented some features of a qualitative comparative analysis of the model associated to the vortex flow technology. In the computational analysis there were used the fast analysis tools of MAPLE11 soft, in order to check the “rare events” and to complete the statistical analysis of the behaviour of the model.     

KamiWaAI – interactive 3D sketching with Java based on Cl(4, 1) conformal model of Euclidean space

This paper introduces the new interactive Java sketching software KamiWaAi, recently developed at the University of Fukui. Its graphical user interface enables the user without any knowledge of both mathematics or computer science, to do full three dimensional “drawings” on the screen. The resulting constructions can be reshaped interactively by dragging its points over the screen. The programming approach is new. KamiWaAi implements geometric objects like points, lines, circles, spheres, etc. directly as software objects (Java classes) of the same name. These software objects are geometric entities mathematically defined and manipulated in a conformal geometric algebra, combining the five dimensions of origin, three space and infinity. Simple geometric products in this algebra represent geometric unions, intersections, arbitrary rotations and translations, projections, distance, etc. To ease the coordinate free and matrix free implementation of this fundamental geometric product, a new algebraic three level approach is presented. Finally details about the Java classes of the new GeometricAlgebra software package and their associated methods are given. KamiWaAi is available for free internet download.