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A solution with a moving singularity for the Fujita equation
The Fujita equation is a type of nonlinear diffusion equation. It is known to exhibit various interesting phenomena, such as ‘blow-up’ where the maximum of a solution can tend to infinity in a finite time. Now Eiji Yanagida from the Department of Mathematics at Tokyo Institute of Technology and Shota Sato from the Mathematical Institute at Tohoku University have found a new solution that is particularly unusual for nonlinear diffusion equations.
No solutions extend to times beyond the blow-up point. On the other hand, the Fujita equation does have a stationary solution with a singularity that is radially symmetric with respect to the singularity point. Eiji Yanagida and Shota Sato have now proved the existence of a solution whose singularity moves along a prescribed curve in time. Mathematically, such a solution is called a weak solution. This is the first example of a time-dependent weak solution of a nonlinear diffusion equation.
The researchers also carefully studied the behavior of singular solutions and found one whose singularity suddenly becomes anomalous. The study of singular solutions will open up a new field of analysis on partial differential equations.
References
- S. Sato and E. Yanagida Solutions with moving singularities for a semilinear parabolic equation J. Differential Equations 246 (2009), 724–748 (10.1016/j.jde.2008.09.004)
- S. Sato and E. Yanagida Forward self-similar solution with a moving singularity for a semilinear parabolic equation Discrete and Continuous Dynamical Systems Series A 26 (2010), 313-331 (10.3934/dcds.2010.26.313)
- S. Sato and E. Yanagida Singular backward self-similar solutions of a semilinear parabolic equation Discrete and Continuous Dynamical Systems Series S 4 (2011), 897–906 (10.3934/dcdss.2011.4.897)
- S. Sato1 and E. Yanagida2 Appearance of anomalous singularities in a semilinear parabolic equation Communications in Pure and Applied Analysis (in press).
Affiliations: 1 Mathematical Institute, Tohoku University, Sendai 980-8578, Japan, 2 Department of Mathematics, Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8551, Japan
The profile of a solution u(x, t) of the Fujita equation with a moving singularity at ξ(t), where t is time, x is the spatial variable in RN.
Factors affecting growth in Thai automotive parts companies
The Thai automotive industry has grown rapidly. Aspects of the industry such as automotive spare parts are experiencing strengthened competition. As a result Thai domestic automotive parts companies need to improve their level of technology effectively in accordance with the demands of assemblers.
Saiki and her colleagues conducted a questionnaire and interview survey relating to technology management in domestic and foreign (Japanese) companies in Thailand. They analysed the factors affecting the growth rate of sales.
The researchers found that small- and medium-sized companies like Thai automotive parts companies need to use rather high-level quality-management techniques. It was also necessary to adopt several proprietary technologies including computer-aided manufacturing (CAM), computer-aided design (CAD) and computerized numerical control machines (CNC), as well as some management technologies to decrease the in-house defect rate. As to human-resource management, higher retention rates seem to result in the establishment of a high sales growth.
Many domestic companies are small- or medium-sized with fewer human resources. However, it seems not only improvement in the level of technology but also the enhancement of employee support is required to raise product quality.
Reference:
・ Authors: Chan-orn Bongsebandhu-phubhakdi, Tomoko Saiki, and Hiroshi Osada.
・ Title of original paper: Management of technology in Thai automotive parts companies.
・ Journal, volume, pages and year: Journal of Advances in Management Research 6, 128-143 (2009).
・ Digital Object Identifier (DOI): 10.1108/09727980911007163
・ Affiliations: Department of Technology Management, Graduate School of Innovation Management.
・ Department website: http://www.mot.titech.ac.jp/
Quantitative production, export and targets for 2010.
Thermoresponsive extraction of cadmium(II) ions by poly(TPEN-NIPA) gels
We have recently shown that poly(TPEN)–NIPA gel effectively extracts soft metal ions such as CdII and f-block metals such as minor actinides from high-level radioactive waste.
Derivatives of TPEN that bear four polymerizable double bonds in the substituent on the pyridine ring have been used as a crosslinker in poly-NIPA gel. However, the optimum structure of the substituent of TPEN is poorly understood.
Yusuke Inaba, Kenji Takeshita at the Research Laboratory for Nuclear Reactors, Tokyo Institute of Technology, and Atsunori Mori and colleagues at the Department of Chemical Science and Engineering, Kobe University have synthesized novel TPEN derivatives and poly(TPEN-NIPA)gels. These gels have been used for the extraction of CdII ions to examine the relationship between gel characteristics and extraction performance.
The temperature-dependent CdII extraction behavior of poly(TPEN-NIPA) gels was examined in the swelling state (5°C) and in the shrinking state (45°C) at pH values of around 2.0 and 6.5.
The high performance of one of the gels, C3b, is noteworthy. It was found to form the strongest gel, probably because of the improved reactivity brought about by the introduction of an electron-donating methyl substituent into the double bond.
These gels could potentially be applied to the separation of minor actinides from high-level radioactive wastes.
Reference:
・ Authors: Yusuke Inaba1, Takayuki Tsumagari2, Tatsuya Kida2, Wataru Watanabe2, Yasutaka Nakajima2, Sachio Fukuoka2, Atsunori Mori2, Tatsuro Matsumura2, Yoshio Nakano4, and Kenji Takeshita1
・ Title of original paper: Thermoresponsive extraction of cadmium(II) ions by poly(TPEN–NIPA) gels. Effect of chain length and branched spacer structure on gel formation and extraction behavior.
・ Journal, volume, pages and year: Polymer Journal 43, 630 (2011).
・ Digital Object Identifier (DOI): 10.1038/pj.2011.38
・ Affiliations: 1Research Laboratory for Nuclear Reactors, Tokyo Institute of Technology, 2Department of Chemical Science and Engineering, Kobe University, 3Nuclear Science and Engineering Directorate, 4Department of Environmental Science and Engineering, Tokyo Institute of Technology.
・ Department website: http://www.nr.titech.ac.jp/~takeshita/Takeshita/English/index_e.html
Synthesis of poly(TPEN–NIPA) gel.
Thermo-responsive swelling and shrinking behaviors of the gel C4.
Thermo-responsive extraction of poly(TPEN-NIPA) gels at 5 ºC and 45 ºC.
Into the Fast Stream: Real-time Web Monitoring with StreamWeb
Web services such as Twitter work by using streaming Web APIs (Application Programming Interfaces) – a set of codes that software programs follow in order to communicate with each other. APIs enable users to send and retrieve streaming data, meaning it is now possible to follow the current status or trends of the world in real-time, such as tracking of infectious disease, crime prediction, or marketing. Various innovative business services are therefore possible if streaming can be monitored successfully. However, for such services to be implemented into a system at present, the performance and scalability of the services will depend on the skills of the computer engineers.
To make this task easier, Toyotaro Suzumura and Tomoaki Oiki based in the Department of Computer Science at Tokyo Institute of Technology, have created a real-time web monitoring system called ‘StreamWeb’ that works alongside a stream computing system called System S developed by IBM Research. The StreamWeb system allows developers to easily input analytical algorithms for a variety of different streaming data without worrying about performance and scalability. StreamWeb also provides real-time web monitoring for massive amounts of data.
The researchers created an application that monitors a list of keywords in Twitter streaming data. The Twitter messages are then displayed, with the specified keywords highlighted, on a Google map showing the physical location where the message was posted. The application can handle nearly 30 thousand Twitter messages per second on a system with 8 computing nodes. This prototype application confirms that web monitoring systems can be built that satisfy the need for high software productivity and can also be used on systems of different scales.
Reference:
・ Authors: Toyotaro Suzumura and Tomoaki Oiki
・ Title of original paper: StreamWeb: Real-Time Web Monitoring with Stream Computing
・ Journal, volume, pages and year: IEEE International Conference on Web Services, ICWS 2011, 620-627, 2011
・ Digital Object Identifier (DOI): 10.1109/ICWS.2011.16
・ Affiliations: Department of Computer Science, Engineering, Graduate School of Information Science and Engineering, Tokyo Institute of Technology
・ Department website: http://www.cs.titech.ac.jp/
Displaying real-time Twitter messages with the word “iPhone” on Google Maps.
