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Articles 1 - 7 of 7
Full-Text Articles in Physical Sciences and Mathematics
Reinforcing The Number Of Disjoint Spanning Trees, Damin Liu, Hong-Jian Lai, Zhi-Hong Chen
Reinforcing The Number Of Disjoint Spanning Trees, Damin Liu, Hong-Jian Lai, Zhi-Hong Chen
Scholarship and Professional Work - LAS
The spanning tree packing number of a connected graph G, denoted by T(G), is the maximum number of edge-disjoint spanning trees of G. In this paper, we determine the minimum number of edges that must be added to G so that the resulting graph has spanning tree packing number at least k, for a given value of k.
A Flexible Solvolysis Experiment For The Undergraduate Organic Laboratory, John J. Esteb, John R. Magers, Luanne M. Mcnulty, Paul Morgan
A Flexible Solvolysis Experiment For The Undergraduate Organic Laboratory, John J. Esteb, John R. Magers, Luanne M. Mcnulty, Paul Morgan
Scholarship and Professional Work - LAS
A simple SN1 reaction is presented that uses bromotriphenylmethane and a range of oxygen-based nucleophiles including water and various alcohols. This procedure represents a process that affords easy isolation of solid products. Typical student yields ranged from 17–128% with the average yield of 50%. Students obtained products with a melting point range of 140 to 164 °C. This procedure offers multiple ways to adapt this experiment from a straight solvolysis reaction to a discovery-based experiment that explores the effect of nucleophile (for a more advanced group) or the method of product isolation.
Collapsible Graphs And Reductions Of Line Graphs, Zhi-Hong Chen, Peter C.B. Lam, Wai-Chee Shiu
Collapsible Graphs And Reductions Of Line Graphs, Zhi-Hong Chen, Peter C.B. Lam, Wai-Chee Shiu
Scholarship and Professional Work - LAS
A graph G is collapsible if for every even subset X ⊆ V ( G ) , G has a subgraph such that G − E ( Γ ) is connected and the set of odd-degree vertices of Γ is X . A graph obtained by contracting all the non-trivial collapsible subgraphs of G is called the reduction of G . In this paper, we characterize graphs of diameter two in terms of collapsible subgraphs and investigate the relationship between the line graph of the reduction and the reduction of the line graph. Our results extend former results in [H.-J. …
Computing Prime Harmonic Sums, Eric Bach, Dominic Klyve, Jonathan P. Sorenson
Computing Prime Harmonic Sums, Eric Bach, Dominic Klyve, Jonathan P. Sorenson
Scholarship and Professional Work - LAS
We discuss a method for computing Σ �≤� 1/�, using time about �2/3 and space about �1/3. It is based on the Meissel-Lehmer algorithm for computing the prime-counting function �(�), which was adapted and improved by Lagarias, Miller, and Odlyzko. We used this algorithm to determine the first point at which the prime harmonic sum first crosses.
The Hamiltonian Index Of Graphs, Yi Hong, Jian-Liang Lin, Zhi-Sui Tao, Zhi-Hong Chen
The Hamiltonian Index Of Graphs, Yi Hong, Jian-Liang Lin, Zhi-Sui Tao, Zhi-Hong Chen
Scholarship and Professional Work - LAS
The Hamiltonian index of a graph G is defined as h ( G ) = min { m : L m ( G ) is Hamiltonian } . In this paper, using the reduction method of Catlin [P.A. Catlin, A reduction method to find spanning Eulerian subgraphs, J. Graph Theory 12 (1988) 29–44], we constructed a graph H ̃ ( m ) ( G ) from G and prove that if h ( G ) ≥ 2 , then h ( G ) = min{ m : H ̃ ( m ) ( G ) has a spanning Eulerian subgraph …
A Simple Sn2 Reaction For The Undergraduate Organic Laboratory, John J. Esteb
A Simple Sn2 Reaction For The Undergraduate Organic Laboratory, John J. Esteb
Scholarship and Professional Work - LAS
A simple procedure for the synthesis of n-butyl naphthyl ether is presented. This procedure represents an easy method for the production of an aryl ether by an SN2 reaction, uses ethanol as an environmentally friendly solvent, and does not require the use of a lachrymator. Product isolation is done by pouring the reaction mixture over ice and collecting the solid by suction filtration. Students typically recover from 7–95% of the ether.
Some Curious Cut-Ups, Jeremiah Farrell, Ivan Moscovich
Some Curious Cut-Ups, Jeremiah Farrell, Ivan Moscovich
Scholarship and Professional Work - LAS
We have noticed a certain kind of n-gon dissection into triangles that has a wonderful property of interest to most puzzlists. Namely that any two triangles have at least one edge in common yet no two triangles need be congruent. In an informal poll of specialists at a recent convention, none of them saw immediately how this could be accomplished. But in fact it is very straightforward.