On total 9-coloring planar graphs of maximum degree seven
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 flexibility of toroidal embeddings
abstract: Two embeddings @J"1 and @J"2 of a graph G in a surface @S are equivalent if there is a homeomorphism of @S to itself carrying @J"1 to @J"2. In this paper, we classify the flexibility of embeddings in the torus with representativity at least 4. We show that if a 3-connected graph G has an embedding @J in the torus with representativity at least 4, then one of the following holds:(i)@J is the unique embedding of G in the torus; (ii)G has three nonequivalent embeddings in the torus, G is the 4-cube Q"4 (or C"4xC"4), and each embedding of G forms a 4-by-4 toroidal grid; (iii)G has two nonequivalent embeddings in the torus, and G can be obtained from a toroidal 4-by-4 grid (faces are 2-colored) by splitting i(i=<16) vertices along one-colored faces and replacing j(j=<16) other colored faces with planar patches.

title: The size of edge chromatic critical graphs with maximum degree 6
abstract: In 1968, Vizing [ (1968) 117–134;  (1968), 125–142] conjectured that for any edge chromatic critical graph G = (V, E) with maximum degree , |E| ≥ 2{( 1)|V| + 3}. This conjecture has been verified for ≤ 5. In this article, by applying the Contract grant sponsor: Middle Tennessee State University Summer Research Grant 2004;  China University of Mining and Technology Science Council;   National Security Agency; Contract grant number: MDA-904-02-1-0096 ;

title: Coloring the Faces of Convex Polyhedra so That Like Colors Are Far Apart
abstract: This paper proves the conjecture of Hornak and Jendrol' that the faces of a convex polyhedron with maximum vertex degree ? can be colored with 1+(?+7)(??1)d colors in such a way that each pair of faces that are distance at most d apart receives different colors.

title: Coloring edges of graphs embedded in a surface of characteristic zero
abstract: Consider graphs that are embeddable in a surface of characteristic zero. Class two graphs of this type with maximum degree Δ ≤ 6 are known to exist. Hind and Zhao showed that such graphs with maximum degree Δ ge; 8 must be class one. This article shows that such graphs with maximum degree Δ = 7 also must be class one, completing the analysis of these surfaces. These are the first surfaces where the maximum degree of class two graphs has been determined.

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: 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.

title: Optimal Spectrum Management in Multiuser Interference Channels
abstract: In this paper, we study the problem of continuous frequency optimal spectrum management in multiuser frequency selective interference channels. We assume that interference is treated as noise by the decoders, and separate encoding is applied. First, a simple pair-wise channel condition for frequency division multiple access schemes to achieve all Pareto optimal points of the rate region is derived. It enables fully distributed global optimal decision making on whether any two users should use orthogonal channels. Next, we present an analytical solution to finding the maximum sum-rate in two-user symmetric frequency flat channels. Generalizing this solution to frequency selective channels, a convex optimization is established that yields the global optimum. Finally, we show that our method generalizes to K-user (K ≥ 2) weighted sum-rate maximization in asymmetric frequency selective channels, and we transform this classic nonconvex optimization to an equivalent convex optimization in the primal domain.

title: MBBNTree Classifier Algorithm Based on Active Learning from Unlabeled Samples
abstract: MBBNTree algorithm, which integrates the advantage of Markov blanket Bayesian networks (MBBN) and decision tree, would behave better performance than other Bayesian networks for classification. But the available training samples with actual classes are not enough for building MBBNTree classifier in practice. 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. In this paper, the MBBNTree classifier algorithm based on active learning would be presented to solve the problem of learning MBBNTree classifier from unlabeled samples. Experimental results show that the proposed algorithm can reach the same accuracy as passive learning with few labeled training examples.

title: Silicon Wafer Defect Extraction Based on Morphological Filter and Watershed Algorithm
abstract: Defect extraction techniques are studied regarding the silicon wafer surface defect. We design a new filter based on multiple structuring elements and suggest an improved marker-based and region merging watershed. To begin with, the filter which generalized close-opening and open-closing filter based on the morphological filter with multiple structuring elements is introduced to eliminate the noise and simplify the image and morphological gradient image while preserving the details. And then in order to reduce the over-segmentation of the watershed algorithm, this paper suggests an improved marker-based and region merging method, region average gray value and edge strength criterion is used in merging operation and has a good effect on segmentation. Finally, the improved watershed algorithm is applied to the filtered gradient image to get the defect contours. The experiments show that this method can eliminate the noises and extract accurately location and closed region contours, which lays a good foundation for defect feature extraction and selection.