On the Nochka-Chen-Ru-Wong Proof of Cartan's Conjecture

In 1982-83, E. Nochka proved a conjecture of Cartan on defects of holomorphic curves in $\Bbb P^n$ relative to a possibly degenerate set of hyperplanes. This was further explained by W. Chen in his 1987 thesis, and subseqently simplified by M. Ru and P.-M. Wong in 1991. The proof involved assigning weights to the hyperplanes. This paper provides a mild simplification of the proof of the construction of the weights, by construing the ``Nochka diagram'' of Ru and Wong as a convex hull.Comment: 6 pages, 1 figure. Reorganized to reflect the submitted version; added a reference to a paper of Nochk

Solitons in the one-dimensional forest fire model

Fires in the one-dimensional Bak-Chen-Tang forest fire model propagate as solitons, resembling shocks in Burgers turbulence. The branching of solitons, creating new fires, is balanced by the pair-wise annihilation of oppositely moving solitons. Two distinct, diverging length scales appear in the limit where the growth rate of trees, $p$, vanishes. The width of the solitons, $w$, diverges as a power law, $1/p$, while the average distance between solitons diverges much faster as $d \sim \exp({\pi}^2/12p)$.Comment: 4 pages with 2 figures include

75 years of engineering: 75th anniversary commemorative publication

published_or_final_versionDays in the Department of Mechanical Engineering E.K.H. Leung Leung, E. K. H. 89Preface 1MessagesAnniversary Photographs and SpeechesList of Sponsors and Donors 285Staff List 288His Excellency Sir David Wilson, KCMG 3Sir Sze-yuen Chung, CBE, JP 4The Hon. Allen Lee 11Dr. R.C.T. Ho 14Professor Y.C. Cheng 16The Hon. H.K. Cheng 21Dr. Wang Gungwu 23Sir S.Y. Chung 25A History of the Faculty Dr. J.A. Clark Clark, J. A. 30ReflectionsEngineering TopicsCurrent ResearchIndustrial Training For Undergraduates 277Reminiscences of My Early Days With the Faculty of Engineering S.Y. King King, S. Y. 69The Don in Action Again E.A. Bruges Bruges, E. A. 72Reminiscences of the Faculty of Engineering K.F. Nip Nip, K. F. 80Personal Reminiscences J. Chiu Chiu, J. 85The Ruminations and Random Thoughts of a 1978 M.SC.(ENG.) Graduate in Industrial Engineering T.C. Hassett Hassett, T. C. 92My Personal Reflections About the Department of Civil and Structural Engineering and Its Future Development E.S.H. Chan Chan, E. S. H. 96The Department of Industrial Engineering - the First Eight Years 1973-81 W.A. Reynolds Reynolds, W. A. 102The Department of Industrial Engineering - Recent Developments 1981-88 N.N.S. Chen Chen, N. N. S. 115A New Department: Computer Science F.Y.L. Chin Chin, F. Y. L. 121Computer Recognition of Putonghua C. Chan and P.Y.S. Cheung Chan, C. Cheung, P. Y. S. 135Cadcam -- What, Which, and How? W.S. Sze, S. F. Tan, and M.F. Yuen Sze, W. S. Tan, S. T. Yuen, M. F. 139Construction Project Management S.M. Rowlinson Rowlison, S. M. 151Development of Electric Vehicles C.C. Chan Chan, C. C. 155The Abatement of Rock Dust Generated By Pneumatic Drills Inside Hand-dug Caissons M Fang Et Al Fang, M. 159The Development of a Novel Electro-rheological Robot Arm Transmission System E.C. Partington and T.N. Wong Partington, E. C. Wong, T. N. 167Maglev Electrical Machines C.T. Choy Choy, C. T. 169Pedemoirography A. Asundi Asundi, A. 175River Indus Hydraulic Model Study J.H.W Lee and A.W Jayawardena Lee, J. H. W. Jayawardena, A. W. 176It's a Material World B.J. Duggan Duggan, B. J. 179Simulation of Container Port Operations D. Sculli and P.K Wong Sculli, D. Wong, P. K. 183Case Studies of Failure Investigations G.W. Greene Greene, G. W. 185Computer Aided Design and Computer Aided Manufacture (CADCAM) W.S. Sze, S. T. Tan, and M.F. Yuen Sze, W. S. Tan, S. T. Yuen, M. F. 187Adhesive Bonded Joints N.N.S. Chen, P.I.F. Niem, and R.C. Lee Chen, N. N. S. Niem, P. I. F. Lee, R. C. 195Application of Artificial Intelligence to Software Engineering T.Y. Chen and T.H. Tse Chen, T. Y. Tse, T. H. 198Biomedical Signal Processing F.H.Y. Chan and F.K Lam Chan, F. H. Y. Lam, F. K. 199Cold Rolling of Thermoplastics N.N.S. Chen, P.I.F. Niem, and Y.W. Lee Chen, N. N. S. Niem, P. I. F. Lee, Y. W. 200Cooling of Polyethylene Bubble A.C.Y. Wong Wong, A. C. Y. 202Design of a Six-axis Robotic Manipulator P.C. Chiu and K.F. Lee Chiu, P. C. Lee, K. F. 203An Easy-to-use and Low-cost Cadcam System For Mould and Die Cavities S.H. Choi Choi, S. H. 212Effects of Fines On Gas Fluidization Properties A.C.Y. Wong Wong, A. C. Y. 213Effects of Moisture On Processing Conditions and Welding Properties of Polyamides A.C.Y. Wong, C.Y. Yue, and C.F. Lau Wong, A. C.Y. Yue, C. Y. Lau, C. F. 215Optimum Blend Ratio of Lldpe Using an Unmodified Conventional Blown Film Line A.C.Y. Wong Wong, A. C. Y. 215Facsimile Processing F.K. Lam Lam, F. K. 216Microcomputer Based Ultrasonic Imaging System F.K. Lam Lam, F. K. 216Weather Satellite Receiving System K.L. Ho and F.K. Lam Ho, K. L. Lam, F. K. 217High-performance Power and Power Semi-conductor Control Systems S.K. Tso Tso, S. K. 218Sensor-based Adaptively Controlled Robotic Systems S.K. Tso Tso, S. K. 218Hydraulics and the Environment J.H.W. Lee and A.W. Jayawardena Lee, J. H. W. Jayawardena, A. W. 219Hypercube Supercomputers C.C. Lau Lau, C. C. 234Impact Micro-viscometry P.L. Wong and S. Lingard Wong, P. L. Lingard, S. 236International Collaboration in Civil and Structural Engineering Y.K. Cheung Cheung, Y. K. 240Moire Interferometry For Deformation Measurement A. Asundi Asundi, A. 243Monitoring Output Performance of Motors W.S. Leung Leung, W. S. 251Self-tuning Controllers C.W. Chan Chan, C. W. 256The Simian Project J.B. Evans Evans, J. B. 261Stresses in Metal Cutting N.N.S. Chen and W.K. Pun Chen, N. N. S. Pun, W. K. 268Trends in the Telecommunication Industry T.I. Yuk and K.W. Tse Yuk, T. I. Tse, K. W. 26

A modification of the Chen-Nester quasilocal expressions

Chen and Nester proposed four boundary expressions for the quasilocal quantities using the covariant Hamiltonian formalism. Based on these four expressions, there is a simple generalization that one can consider, so that a two parameter set of boundary expressions can be constructed. Using these modified expressions, a nice result for gravitational energy-momentum can be obtained in holonomic frames.Comment: 11 page