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61.
Donald J. Collins 《Mathematische Annalen》1978,237(3):233-241
LetH=〈a,b;a k =b l 〉, wherek,l≧2 andk+l>4. McCool and Pietrowski have proved that any pair of generators forH is Nielsen equivalent to a pairx=a r andy=b s where $$(a){\text{ }}gcd(r, s) = gcd(r, k) = gcd(s, l) = 1,$$ $$(b){\text{ }}0< 2r \leqq ks{\text{ }}and{\text{ }}0< 2s \leqq lr.$$ In terms ofx andy,H can be presented as $$G = \left\langle {x,{\text{ }}y;{\text{ }}x^{ks} = y^{lr} ,\left[ {x,{\text{ }}y^l } \right] = \left[ {x^k ,{\text{ }}y} \right] = 1} \right\rangle$$ and Zieschang has shown that ifr=1 ors=1, thenH can be defined by a single relation inx andy. We establish the exact converse of Zieschang's result, namely thatH is not defined by a single relation inx andy unlessr=1 ors=1. The proof is based on an observation of Magnus which associates polynomials with relators and some elementary facts about cyclotomic polynomials. 相似文献
62.
63.
Joachim Schaefer William A. Lester Donald Kouri Charles A. Wells 《Chemical physics letters》1974,24(2):185-190
Integral cross sections for pure rotational and vibrational-rotational excitation of H2(X1Σ+g) by Li+(1S) impact are computed by close-coupling methods at 0.2, 0.6, and 1.2 eV in the c.m. system using vibrational functions that are numerical solutions of the one-dimensional radial Schrödinger equation for harmonic, Morse, and adiabatically corrected Kolos-Wolniewicz (KW) potential functions. Comparison of results employing KW and Morse functions shows excellent agreement for all transitions studied. Findings using harmonic oscillator functions, however, differ noticeably from KW and Morse values for vibrational (0 → 1) and very large rotational (Δj = 10) transitions, but are satisfactory for lower order (0 → 2, 4, 6, 8) rotational transitions. 相似文献
64.
Solutions of selenium(IV) standards with different acid matrices were stored in containers constructed of boosilicate glass, conventional polyethylene, and fluorinated ethylenepropylene (teflon FEP). After 50 days of storage in FEP, there were highly significant losses of Se(IV) from standards in either 5% HCl/5% H2SO4, or 5% H2SO4. Increasing the hydrochloric acid concentration, e.g., 15% HCl/5% H2SO4, greatly reduced this loss. Addition of selenium-75 (selenate-free) indicated that the losses did not result from physical adsorption onto container surfaces. It is shown that the losses were caused by oxidation of Se(IV) to Se(VI). 相似文献
65.
T. Bernard Tate 《The Journal of the Operational Research Society》1977,28(4):765-779
Good technique, i.e. competence in carrying out operational research, is as vital for the practitioner to acquire as competence in the traditional ‘techniques’. It is suggested that universities should teach students how to conduct simple projects prior to alerting them to more sophisticated methodological issues.As an aid to this task, the traditional five or six parts of an operational research project are broken down and extended into 39 steps, and regrouped into three phases. Also, five skills are identified as being conceptually essential to "good" operational research, which students can develop through tackling suitable case studies. 相似文献
66.
67.
The MSR (muonium spin rotation) technique was used to measure the chemical reaction rate for Mu + F2 → MuF + F in N2 moderator at ≈ 1 atm from 295 to 383 K giving the Arrhenius expression: log10k (?/mole s) = (10.83 ± 0.20) - (200 ± 50)/T, with k = (1.46 ± 0.11) × 1010 ?/mole s at 300 K. This is at least 6.8 times the room temperature rate constant for the analogous H atom reaction. The measured activation energy and enhancement over the H reaction rate are indicative of significant tunnelling in the Mu reaction, in agreement with the recent collinear quantum mechanical calculations of Connor et al. 相似文献
68.
Haiwen Zhang David W. Norman Tracey M. Wentzell Alison M. Irving Janet P. Edwards Susan L. Wheaton Christopher M. Vogels Stephen A. Westcott Felix J. Baerlocher Andreas Decken 《Transition Metal Chemistry》2005,30(1):63-68
Reactions of salicylaldehydes with boronate ester derivatives of aniline have been examined. Addition of these Schiff base ligands to palladium acetate or Na2PdCl4 afforded novel boron-containing trans-bis(N-arylsalicylaldiminato) palladium complexes.Condensation of salicylaldehyde (2-HOC6H4C(O)H) with H2NC6H4Bpin (pin=1,2-O2C2Me4) afforded the boron-containing Schiff bases, 2-HOC6H4C(H)=NC6H4Bpin (1–3a). Similar reactivity with 2-hydroxy-5-nitrobenzaldehyde and 2-hydroxy-1-naphthaldehyde gave the corresponding Schiff bases (1-3b) and (1-3c), respectively. Reaction of Schiff bases (2) and (3) with palladium acetate or Na2PdCl4 afforded complexes of the type PdL2
(4,5), where L=deprotonated Schiff base. The molecular structure of the nitro-salicylaldehyde 4-Bpin palladium complex (5b) was characterized by an X-ray diffraction study. All new palladium compounds have been characterized fully and tested for their antifungal activity against Aspergillus niger and Aspergillus flavus. 相似文献
69.
70.
The use of electrolytically generated silver(II) as a coulometric titrant has been studied. Difficulties arising from the current efficiency for generation of silver (II) at a platinum or gold electrode and from the reduction of silver(II) by water, have been overcome. The precautions necessary for accurate titrations of oxalic acid, cerium(III), arsenic(III) and vanadium(IV) by amperometric or potentiometric methods are detailed. Manganese and chromium could not be determined directly. Substances which reduce nitric acid could be determined if care was taken. 相似文献