On Simultaneous Edge-Face Colorings of Plane Graphs

title: On total 9-coloring planar graphs of maximum degree seven
abstract: Given a graph G, a total k-coloring of G is a simultaneous coloring of the vertices and edges ofGwith at most k colors. If ∆(G) is the maximum degree ofG, then no graph has a total ∆-coloring, but Vizing conjectured that every graph has a total (∆ + 2)-coloring. This Total Coloring Conjecture remains open even for planar graphs. This article proves one of the two remaining planar cases, showing that every planar (and projective) graph with ∆ ≤ 7 has a total 9-coloring by means of the discharging method.

title: On the edge-reconstruction of graphs embedded in surfaces IV
abstract: In this paper, by applying the discharging method, we give simple proofs that (1) every n-vertex graph with minimum degree at least 3 and girth at least 5 that is embeddable in a surface Σ of Euler characteristic at least -n/8 is edge-reconstructible, and (2) every n-vertex graph with minimum degree at least 4 that is embeddable without faces of length at most 3 in a surface Σ of Euler characteristic at least -n/6 is edge-reconstructible.

title: On Diagonally 10-Coloring Plane Triangulations
abstract: This article shows that the vertices of a plane triangulation may be colored with 10 colors such that every pair of vertices has different colors if they are either adjacent or diagonal, that is, that they are not adjacent but are adjacent to two faces which share an edge. This improves a result of Borodin, who showed that 11 colors were sufficient.

title: On the Edge Reconstruction of Graphs Embedded in Surfaces, III,
abstract: In this paper, we prove that if a connected graphGembeddable in a surface?of characteristic?(?) satisfies (1) the minimum degree ofG?5, (2) |V(G)|??43?(?), thenGis edge reconstructible. A direct consequence of the above result is that a triangulationGof a surface of characteristic?(?) is edge reconstructible if |V(G)|??43?(?).

title: On spanning trees and walks of low maximum degree

title: Improvement of the Damaged Thermowell of the Monju Fast-Breeder Reactor Based on Vibration Analysis
abstract: In December 1995, the thermowell in the secondary cooling system of the Japanese fast-breeder reactor Monju was damaged, resulting in a sodium leak. Sodium flow was thought to have produced a vibration in the thermowell that then caused high-cycle fatigue that eventually destroyed the thermowell. Using the finite element method, the natural frequency of the thermowell was found to be approximately 230 Hz, which is in the region of resonance of the fluid vibration. Next, in a theoretical study, the authors altered the position at which the diameter of the thermowell changes and examined the resulting natural frequencies. They also studied the effects of thickness and diameter on the natural frequency of the thermowell and examined the case for a truncated conical thermowell. The results indicate that production of a thermowell that is not affected by vibration due to resonance is possible. This paper recommends improved shapes for the thermowell.

title: Evolving Model for Small-World Network Based on Benefit Choice
abstract: Based on reviewing the research progress of evolving model for small-world network, the defects of present studies were pointed out. Taking a square grid as the basis, an evolving model for small-world network based on benefit choice was built. This model is different from other papers in which limitation of vector' degree was considered. Then, the author proposed a simulation scheme and compared the network generated by simulation with a same scale random network. The results show that this network has small-world characteristic. Finally, several directions were given.

title: Research on Query-by-Committee Method of Active Learning and Application
abstract: Active learning aims at reducing the number of training examples to be labeled by automatically processing the unlabeled examples, then selecting the most informative ones with respect to a given cost function for a human to label. The major problem is to find the best selection strategy function to quickly reach high classification accuracy. Query-by-Committee (QBC) method of active learning is less computation than other active learning approaches, but its classification accuracy can not achieve the same high as passive learning. In this paper, a new selection strategy for the QBC method is presented by combining Vote Entropy with Kullback-Leibler divergence. Experimental results show that the proposed algorithm is better than previous QBC approach in classification accuracy. It can reach the same accuracy as passive learning with few labeled training examples.

title: Recursive Algorithms for a Novel Identification Criterion
abstract: A new identification criterion is concerned for disturbed system with color noise in this paper. The cost function considers both the errors between the actual outputs and the estimation result and the difference of each estimation error. Under this performance function, a new recursive algorithm DSCN (Disturbed System with Color Noise) is proposed. It could reduce the influence of noise in system identification, further decrease the prediction error. Several simulation examples are given to illustrate the method's anti-disturbance performance.

title: Identification of Multi-dimensional System based on a Novel Criterion
abstract: A device uses two laser beams to assist in parking a vehicle having a windshield at a desired distance relative to a surface forward of the vehicle, such as the wall of a garage. Independent adjustment means are preferably provided for angling one or both of the first and second beams so as to converge in a localized region of the surface forward of the vehicle when the vehicle is positioned at a desired distance. The preferred embodiment further includes means for mounting the device to a visor within the vehicle, such that the first and second beams pass through the windshield. A momentary contact button on a bottom panel of the enclosure may then be used to activate the laser by squeezing the device against the visor, if so mounted. Within the enclosure there is supported a mirror, prism or other light re-directing element in the path of one of the first and second beams prior to exiting enclosure causing the two beams to converge in a localized region of the wall when the vehicle is parked at a desired distance therefrom. The mirror and beamsplitter are preferably disposed on independently adjustable mounts to assist in fixing the desired distance. As a further option, a dispersive optical element such as a lens may be disposed in the path of one of the first and second beams causing that beam to form a line on the surface forward of the vehicle. Method aspects of the invention are also disclosed.