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1.
In the classical channel assignment problem, transmitters that are sufficiently close together are assigned transmission frequencies that differ by prescribed amounts, with the goal of minimizing the span of frequencies required. This problem can be modeled through the use of an L(2,1)-labeling, which is a function f from the vertex set of a graph G to the non-negative integers such that |f(x)-f(y)|? 2 if xand y are adjacent vertices and |f(x)-f(y)|?1 if xand y are at distance two. The goal is to determine the λ-number of G, which is defined as the minimum span over all L(2,1)-labelings of G, or equivalently, the smallest number k such that G has an L(2,1)-labeling using integers from {0,1,…,k}. Recent work has focused on determining the λ-number of generalized Petersen graphs (GPGs) of order n. This paper provides exact values for the λ-numbers of GPGs of orders 5, 7, and 8, closing all remaining open cases for orders at most 8. It is also shown that there are no GPGs of order 4, 5, 8, or 11 with λ-number exactly equal to the known lower bound of 5, however, a construction is provided to obtain examples of GPGs with λ-number 5 for all other orders. This paper also provides an upper bound for the number of distinct isomorphism classes for GPGs of any given order. Finally, the exact values for the λ-number of n-stars, a subclass of the GPGs inspired by the classical Petersen graph, are also determined. These generalized stars have a useful representation on Möebius strips, which is fundamental in verifying our results. 相似文献
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3.
C.A. Cody R.C. Levitt R.K. Khanna Philip J. Miller 《Journal of solid state chemistry》1978,26(3):293-309
The infrared and Raman spectra of NaH3(SeO3)2 and NaD3(SeO3)2 have been recorded from 24 to 300°K. The interpretation, assignments, and analysis of the spectral studies are presented on the paraelectric α phase (proton disordered), ferroelectric β phase (proton ordered) and ferroelectric γ phase (proton ordered). A discussion of a newly proposed proton-triggered phase transition mechanism and a possible origin of the hydrogen-bonded OH stretching region of KH2PO4-type ferroelectrics is given. 相似文献
4.
Determination of methamphetamine enantiomer ratios in urine by gas chromatography-mass spectrometry. 总被引:2,自引:0,他引:2
J T Cody 《Journal of chromatography. A》1992,580(1-2):77-95
5.
Wu Z Zhang XJ Cody RB Wolfe RR 《European journal of mass spectrometry (Chichester, England)》2004,10(5):619-623
The application of time-of-flight mass spectrometry to isotope ratio measurements has been limited by the relatively low dynamic range of the time-to-digital converter detectors available on commercial LC/ToF-MS systems. Here we report the measurement of phenylalanine isotope ratio enrichment by using a new LC/ToF-MS system with wide dynamic range. Underivatized phenylalanine was injected onto a C18 column directly with 0.1% formic acid/acetonitrile as the mobile phase. The optimal instrument parameters for the time-of-flight mass spectrometer were determined by tuning the instrument with a phenylalanine standard. The accuracy of the isotope enrichment measurement was determined by the injection of standard solutions with known isotope ratios ranging from 0.02% to 9.2%. A plot of the results against the theoretical values gave a linear curve with R2 of 0.9999. The coefficient of variation for the isotope ratio measurement was below 2%. The method is simple, rapid, and accurate and presents an attractive alternative to traditional GC/MS applications. 相似文献
6.
7.
Dickerson CA Fisher MJ Sykora RE Albrecht-Schmitt TE Cody JA 《Inorganic chemistry》2002,41(4):640-642
The compound K(3)PSe(4).2Se(6) was synthesized at 110 degrees C via solventothermal techniques from binary starting materials and Se in acetonitrile. The compound crystallizes in the space group Fd macro 3 of the cubic system with eight formula units in a cell with a dimension of a = 16.415(2) A at T = 193 K. The structure contains an unusual intermixing of ionic and uncharged species. The selenophosphate tetrahedral trianions PSe(4)(3-) are surrounded by potassium cations; other potassium cations in the structure are coordinated to 12 selenium atoms from four Se(6) rings in a tetrahedral arrangement. There are no short contacts between adjacent selenium rings. Heating the same reaction mixture to 160 degrees C results in the formation of only needles of trigonal selenium. 相似文献
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9.
John G. D'Angelo Jeremy A. Cody Christian Larrabee Danica J. Ostrander Kyle W. Rugg Donna Mamangun 《合成通讯》2013,43(23):3224-3232
Herein, we report new reactivity of the conducting polymer, poly-(3,4-ethylenedioxy thiophene) (PEDOT), where PEDOT mediates a Ritter reaction between alcohols and acetonitrile. The yields were variable and in most cases competitive with results obtained using sulfuric acid. Attempts at a stoichiometric reaction between benzonitrile and diphenylmethanol are also reported herein. Finally, described here are preliminary mechanistic studies that suggest PEDOT is behaving as an alcohol-selective or specific Lewis acid. Supplementary materials are available for this article. Go to the publisher's online edition of Synthetic Communications® for full experimental and spectral details. 相似文献
10.
Prof. Li Chen Genevieve E. Mullen Myriam Le Roch Cody G. Cassity Prof. Nicolas Gouault Prof. Henry Y. Fadamiro Prof. Robert E. Barletta Prof. Richard A. O'Brien Prof. Richard E. Sykora Prof. Alexandra C. Stenson Prof. Kevin N. West Howard E. Horne Jeffrey M. Hendrich Kang Rui Xiang Prof. James H. Davis Jr. 《Angewandte Chemie (International ed. in English)》2014,53(44):11762-11765
The practical utility of ionic liquids (ILs) makes the absence (heretofore) of reported examples from nature quite puzzling, given the facility with which nature produces many other types of exotic but utilitarian substances. In that vein, we report here the identification and characterization of a naturally occurring protic IL. It can be formed during confrontations between the ants S. invicta and N. fulva. After being sprayed with alkaloid‐based S. invicta venom, N. fulva detoxifies by grooming with its own venom, formic acid. The mixture is a viscous liquid manifestly different from either of the constituents. Further, we find that the change results as a consequence of formic acid protonation of the N centers of the S. invicta venom alkaloids. The resulting mixed‐cation ammonium formate milieu has properties consistent with its classification as a protic IL. 相似文献