Non-reduced excepticnal algebras with a one-dimensional root space

Author(s):  
George B. Seligman
Keyword(s):  
2016 ◽  
Vol 09 (04) ◽  
pp. 1650070 ◽  
Author(s):  
K. Jayalakshmi ◽  
G. Lakshmi Devi

We give a description of a 2-torsion free Vinberg ([Formula: see text]) ring [Formula: see text]. If every nonzero root space of [Formula: see text] for [Formula: see text] is one-dimensional where [Formula: see text] is a split abelian Cartan subring of [Formula: see text] which is nil on [Formula: see text] then [Formula: see text] is a Lie ring isomorphic to [Formula: see text]. This generalizes the known result obtained by Myung for the case that [Formula: see text] is a 2-torsion free Vinberg ([Formula: see text]) ring and is power associative. We also give a condition that a Levi factor [Formula: see text] of [Formula: see text] be an ideal of [Formula: see text] when the solvable radical of [Formula: see text] is nilpotent. We apply these results for reductive case of [Formula: see text].


1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.


Author(s):  
Teruo Someya ◽  
Jinzo Kobayashi

Recent progress in the electron-mirror microscopy (EMM), e.g., an improvement of its resolving power together with an increase of the magnification makes it useful for investigating the ferroelectric domain physics. English has recently observed the domain texture in the surface layer of BaTiO3. The present authors ) have developed a theory by which one can evaluate small one-dimensional electric fields and/or topographic step heights in the crystal surfaces from their EMM pictures. This theory was applied to a quantitative study of the surface pattern of BaTiO3).


Author(s):  
Peter Sterling

The synaptic connections in cat retina that link photoreceptors to ganglion cells have been analyzed quantitatively. Our approach has been to prepare serial, ultrathin sections and photograph en montage at low magnification (˜2000X) in the electron microscope. Six series, 100-300 sections long, have been prepared over the last decade. They derive from different cats but always from the same region of retina, about one degree from the center of the visual axis. The material has been analyzed by reconstructing adjacent neurons in each array and then identifying systematically the synaptic connections between arrays. Most reconstructions were done manually by tracing the outlines of processes in successive sections onto acetate sheets aligned on a cartoonist's jig. The tracings were then digitized, stacked by computer, and printed with the hidden lines removed. The results have provided rather than the usual one-dimensional account of pathways, a three-dimensional account of circuits. From this has emerged insight into the functional architecture.


Author(s):  
A.Q. He ◽  
G.W. Qiao ◽  
J. Zhu ◽  
H.Q. Ye

Since the first discovery of high Tc Bi-Sr-Ca-Cu-O superconductor by Maeda et al, many EM works have been done on it. The results show that the superconducting phases have a type of ordered layer structures similar to that in Y-Ba-Cu-O system formulated in Bi2Sr2Can−1CunO2n+4 (n=1,2,3) (simply called 22(n-1) phase) with lattice constants of a=0.358, b=0.382nm but the length of c being different according to the different value of n in the formulate. Unlike the twin structure observed in the Y-Ba-Cu-O system, there is an incommensurate modulated structure in the superconducting phases of Bi system superconductors. Modulated wavelengths of both 1.3 and 2.7 nm have been observed in the 2212 phase. This communication mainly presents the intergrowth of these two kinds of one-dimensional modulated structures in 2212 phase.


Author(s):  
J. Fink

Conducting polymers comprises a new class of materials achieving electrical conductivities which rival those of the best metals. The parent compounds (conjugated polymers) are quasi-one-dimensional semiconductors. These polymers can be doped by electron acceptors or electron donors. The prototype of these materials is polyacetylene (PA). There are various other conjugated polymers such as polyparaphenylene, polyphenylenevinylene, polypoyrrole or polythiophene. The doped systems, i.e. the conducting polymers, have intersting potential technological applications such as replacement of conventional metals in electronic shielding and antistatic equipment, rechargable batteries, and flexible light emitting diodes.Although these systems have been investigated almost 20 years, the electronic structure of the doped metallic systems is not clear and even the reason for the gap in undoped semiconducting systems is under discussion.


Author(s):  
Edson de Faria ◽  
Welington de Melo
Keyword(s):  

2001 ◽  
Vol 22 (5) ◽  
pp. 35-40 ◽  
Author(s):  
D. C. Look Jr ◽  
Arvind Krishnan

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