Solution of Vizing's Problem on Interchanges for Graphs with Maximum Degree 4 and Related Results

Let $G$ be a Class 1 graph with maximum degree $4$ and let $t\geq 5$ be an integer. We show that any proper $t$-edge coloring of $G$ can be transformed to any proper $4$-edge coloring of $G$ using only transformations on $2$-colored subgraphs (so-called interchanges). This settles the smallest previously unsolved case of a well-known problem of Vizing on interchanges, posed in 1965. Using our result we give an affirmative answer to a question of Mohar for two classes of graphs: we show that all proper $5$-edge colorings of a Class 1 graph with maximum degree 4 are Kempe equivalent, that is, can be transformed to each other by interchanges, and that all proper 7-edge colorings of a Class 2 graph with maximum degree 5 are Kempe equivalent

Record of Decision, Council Bluffs Interstate System(I-29, I-80 and I-480) Improvements Project, October 15, 2005

The Federal Highway Administration (FHWA) approves the selection of the Reconstruction of All or Part of the Interstate (Construction Alternative) as the Preferred Alternative to provide improvements to the interstate system in the Omaha/Council Bluffs metropolitan area, extending across the Missouri River on Interstate 80 to east of the Interstate 480 interchange in Omaha, Nebraska. The study considered long-term, broad-based transportation improvements along Interstate I-29 (I-29), I-80, and I-480, including approximately 18 mainline miles of interstate and 14 interchanges (3 system, 11 service), that would add capacity and correct functional issues along the mainline and interchanges and upgrade the I-80 Missouri River Crossing

On the interchange of alternating-amplitude pulsation cycles

We characterized the time intervals between the interchanges of the alternating high- and low-amplitude extrema of three RV Tauri and three RR Lyrae stars.Comment: 2 pages, Proceedings of the 301st IAU Symposium, Precision Asteroseismology, August 201

T-Duality in Sigma Models with Kaluza-Klein Metric as Electric-Magnetic Duality

It is shown that the T-duality in \sigma-model with Kaluza-Klein metric, without or with a torsion term, can be interpreted as electric-magnetic duality for some of their solitonic solutions. Actually Buscher's duality transformation interchanges the topological and Noether charges.Comment: 12 Pages, Late

An Equivalence Between Momentum and Charge in String Theory

It is shown that for a translationally invariant solution to string theory, spacetime duality interchanges the momentum in the symmetry direction and the axion charge per unit length. As one application, we show explicitly that charged black strings are equivalent to boosted (uncharged) black strings. The extremal black strings (which correspond to the field outside of a fundamental macroscopic string) are equivalent to plane fronted waves describing strings moving at the speed of light.Comment: 10 page