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First, the basic concept of the vector derivative in geometric algebra is introduced. Second, beginning with the Fourier transform
on a scalar function we generalize to a real Fourier transform on Clifford multivector-valued functions
Third, we show a set of important properties of the Clifford Fourier transform on Cl3,0 such as differentiation properties, and the Plancherel theorem. Finally, we apply the Clifford Fourier transform properties
for proving an uncertainty principle for Cl3,0 multivector functions. 相似文献
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Relaxation of toroidal discharges is described by the principle of minimum energy dissipation together with the constraint
of conserved global helicity. The resulting Euler-Lagrange equation is solved in toroidal coordinates for an axisymmetric
torus by expressing the solutions in terms of Chandrasekhar-Kendall (C-K) eigenfunctions analytically continued in the complex
domain. The C-K eigenfunctions are obtained as hypergeometric functions that are solutions of scalar Helmholtz equation in
toroidal coordinates in the large aspect-ratio approximation. Equilibria are constructed by assuming the current to vanish
at the edge of plasma. For the m=0, n=0 (m and n are the poloidal and toroidal mode numbers respectively) relaxed states, the magnetic field, current, q (safety factor) and pressure profiles are calculated for a given value of aspect-ratio of the torus and for different values
of the eigenvalue λ
r
0. The new feature of the present model is that solutions allow for both tokamak as well as RFP-like behaviour with increase
in the values of λ
r
0, which is related directly to volt-sec in the experiment. 相似文献
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John L. Dillon Richard H. Spector Gary D. Madding Mary E. Wire 《Journal of heterocyclic chemistry》1993,30(3):707-713
Two new and improved syntheses of the antiarrhythmic drug Encainide, 1 , are presented. The first approach is based on the condensation of 2-picolyllithium with the p-anisoyl amide of methyl anthranilate, 3 , followed by a series of catalytic hydrogenations and methylation. The second route relies on a particularly facile condensation reaction between N-methylpicolinium methyl sulfate and o-nitrobenzaldehyde to produce the alcohol 17c in high yield which is converted to the olefin 18c by a novel dehydration procedure and then to the final molecule, by catalytic hydrogenation over platinum followed by acylation. 相似文献
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Sandip N.Gavade Ravi S.Balaskar Madhav S.Mane Pramod N.Pabrekar Murlidhar S.Shingare Dhananjay V.Mane 《中国化学快报》2011,22(6):675-678
The coupling reaction of phenylurea with different functionalized aryl halides in the presence of air stable CuI,N,N-dimethylethylenediamine as a ligand,and K3PO4 as a base gives symmetrical and unsymmetrical diarylureas in relatively high yields.This method is milder than the palladium catalyzed arylation and avoids the use of toxic phosphine ligands. 相似文献
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Helane?MS?Costa Augusto?CV?Freitas Júnior Ian?PG?Amaral Izaura?Y?Hirata Patrícia?MG?Paiva Luiz?B?CarvalhoJr Vitor?Oliveira Ranilson?S?BezerraEmail author 《Chemistry Central journal》2013,7(1):166